Trigonometric functions: Difference between revisions

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If your language has a library or built-in functions for trigonometry, show examples of sine, cosine, tangent, and their inverses using the same angle in radians and degrees.

For the non-inverse functions, each radian/degree pair should use arguments that evaluate to the same angle (that is, it's not necessary to use the same angle for all three regular functions as long as the two sine calls use the same angle).

For the inverse functions, use the same number and convert its answer to radians and degrees.

If your language does not have trigonometric functions available or only has some available, write functions to calculate the functions based on any known approximation or identity.

ACL2

This example is incomplete. Please ensure that it meets all task requirements and remove this message.

(This doesn't have the inverse functions; the Taylor series for those take too long to converge.)

<lang Lisp>(defun fac (n)

  (if (zp n)
      1
      (* n (fac (1- n)))))

(defconst *pi-approx*

  (/ 3141592653589793238462643383279
     (expt 10 30)))

(include-book "arithmetic-3/floor-mod/floor-mod" :dir :system)

(defun dgt-to-str (d)

  (case d
        (1 "1") (2 "2") (3 "3") (4 "4") (5 "5")
        (6 "6") (7 "7") (8 "8") (9 "9") (0 "0")))

(defmacro cat (&rest args)

  `(concatenate 'string ,@args))

(defun num-to-str-r (n)

  (if (zp n)
      ""
      (cat (num-to-str-r (floor n 10))
           (dgt-to-str (mod n 10)))))

(defun num-to-str (n)

  (cond ((= n 0) "0")
        ((< n 0) (cat "-" (num-to-str-r (- n))))
        (t (num-to-str-r n))))

(defun pad-with-zeros (places str lngth)

  (declare (xargs :measure (nfix (- places lngth))))
  (if (zp (- places lngth))
      str
      (pad-with-zeros places (cat "0" str) (1+ lngth))))

(defun as-decimal-str (r places)

  (let ((before (floor r 1))
        (after (floor (* (expt 10 places) (mod r 1)) 1)))
       (cat (num-to-str before)
            "."
            (let ((afterstr (num-to-str after)))
                 (pad-with-zeros places afterstr
                            (length afterstr))))))

(defun taylor-sine (theta terms term)

  (declare (xargs :measure (nfix (- terms term))))
  (if (zp (- terms term))
      0
      (+ (/ (*(expt -1 term) (expt theta (1+ (* 2 term))))
            (fac (1+ (* 2 term))))
         (taylor-sine theta terms (1+ term)))))

(defun sine (theta)

  (taylor-sine (mod theta (* 2 *pi-approx*))
                20 0)) ; About 30 places of accuracy

(defun cosine (theta)

  (sine (+ theta (/ *pi-approx* 2))))

(defun tangent (theta)

  (/ (sine theta) (cosine theta)))

(defun rad->deg (rad)

  (* 180 (/ rad *pi-approx*)))

(defun deg->rad (deg)

  (* *pi-approx* (/ deg 180)))

(defun trig-demo ()

  (progn$ (cw "sine of pi / 4 radians:    ")
          (cw (as-decimal-str (sine (/ *pi-approx* 4)) 20))
          (cw "~%sine of 45 degrees:        ")
          (cw (as-decimal-str (sine (deg->rad 45)) 20))
          (cw "~%cosine of pi / 4 radians:  ")
          (cw (as-decimal-str (cosine (/ *pi-approx* 4)) 20))
          (cw "~%tangent of pi / 4 radians: ")
          (cw (as-decimal-str (tangent (/ *pi-approx* 4)) 20))
          (cw "~%")))</lang>

sine of pi / 4 radians:    0.70710678118654752440
sine of 45 degrees:        0.70710678118654752440
cosine of pi / 4 radians:  0.70710678118654752440
tangent of pi / 4 radians: 0.99999999999999999999

ActionScript

Actionscript supports basic trigonometric and inverse trigonometric functions via the Math class, including the atan2 function, but not the hyperbolic functions. <lang ActionScript>trace("Radians:"); trace("sin(Pi/4) = ", Math.sin(Math.PI/4)); trace("cos(Pi/4) = ", Math.cos(Math.PI/4)); trace("tan(Pi/4) = ", Math.tan(Math.PI/4)); trace("arcsin(0.5) = ", Math.asin(0.5)); trace("arccos(0.5) = ", Math.acos(0.5)); trace("arctan(0.5) = ", Math.atan(0.5)); trace("arctan2(-1,-2) = ", Math.atan2(-1,-2)); trace("\nDegrees") trace("sin(45) = ", Math.sin(45 * Math.PI/180)); trace("cos(45) = ", Math.cos(45 * Math.PI/180)); trace("tan(45) = ", Math.tan(45 * Math.PI/180)); trace("arcsin(0.5) = ", Math.asin(0.5)*180/Math.PI); trace("arccos(0.5) = ", Math.acos(0.5)*180/Math.PI); trace("arctan(0.5) = ", Math.atan(0.5)*180/Math.PI); trace("arctan2(-1,-2) = ", Math.atan2(-1,-2)*180/Math.PI); </lang>

Ada

Ada provides library trig functions which default to radians along with corresponding library functions for which the cycle can be specified.
The examples below specify the cycle for degrees and for radians.
The output of the inverse trig functions is in units of the specified cycle (degrees or radians). <lang ada>with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions; with Ada.Float_Text_Io; use Ada.Float_Text_Io; with Ada.Text_IO; use Ada.Text_IO;

procedure Trig is

  Degrees_Cycle : constant Float := 360.0;
  Radians_Cycle : constant Float := 2.0 * Ada.Numerics.Pi;
  Angle_Degrees : constant Float := 45.0;
  Angle_Radians : constant Float := Ada.Numerics.Pi / 4.0;
  procedure Put (V1, V2 : Float) is
  begin
     Put (V1, Aft => 5, Exp => 0);
     Put (" ");
     Put (V2, Aft => 5, Exp => 0);
     New_Line;
  end Put;

begin

  Put (Sin (Angle_Degrees, Degrees_Cycle), 
       Sin (Angle_Radians, Radians_Cycle));
  Put (Cos (Angle_Degrees, Degrees_Cycle), 
       Cos (Angle_Radians, Radians_Cycle));
  Put (Tan (Angle_Degrees, Degrees_Cycle), 
       Tan (Angle_Radians, Radians_Cycle));
  Put (Cot (Angle_Degrees, Degrees_Cycle), 
       Cot (Angle_Radians, Radians_Cycle));
  Put (ArcSin (Sin (Angle_Degrees, Degrees_Cycle), Degrees_Cycle), 
       ArcSin (Sin (Angle_Radians, Radians_Cycle), Radians_Cycle));
  Put (Arccos (Cos (Angle_Degrees, Degrees_Cycle), Degrees_Cycle), 
       Arccos (Cos (Angle_Radians, Radians_Cycle), Radians_Cycle));
  Put (Arctan (Y => Tan (Angle_Degrees, Degrees_Cycle)),
       Arctan (Y => Tan (Angle_Radians, Radians_Cycle)));
  Put (Arccot (X => Cot (Angle_Degrees, Degrees_Cycle)), 
       Arccot (X => Cot (Angle_Degrees, Degrees_Cycle)));

end Trig;</lang>

Output:

 0.70711  0.70711
 0.70711  0.70711
 1.00000  1.00000
 1.00000  1.00000
45.00000  0.78540
45.00000  0.78540
45.00000  0.78540
45.00000  0.78540

ALGOL 68

Translation of: C

Works with: ALGOL 68 version Standard - no extensions to language used

Works with: ALGOL 68G version Any - tested with release mk15-0.8b.fc9.i386

Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8.8d.fc9.i386

<lang algol68>main:(

 REAL pi = 4 * arc tan(1);
 # Pi / 4 is 45 degrees. All answers should be the same. #
 REAL radians = pi / 4;
 REAL degrees = 45.0;
 REAL temp;
 # sine #
 print((sin(radians), " ", sin(degrees * pi / 180), new line));
 # cosine #
 print((cos(radians), " ", cos(degrees * pi / 180), new line));
 # tangent #
 print((tan(radians), " ", tan(degrees * pi / 180), new line));
 # arcsine #
 temp := arc sin(sin(radians));
 print((temp, " ", temp * 180 / pi, new line));
 # arccosine #
 temp := arc cos(cos(radians));
 print((temp, " ", temp * 180 / pi, new line));
 # arctangent #
 temp := arc tan(tan(radians));
 print((temp, " ", temp * 180 / pi, new line))

)</lang>

Output:

+.707106781186548e +0  +.707106781186548e +0
+.707106781186548e +0  +.707106781186548e +0
+.100000000000000e +1  +.100000000000000e +1
+.785398163397448e +0  +.450000000000000e +2
+.785398163397448e +0  +.450000000000000e +2
+.785398163397448e +0  +.450000000000000e +2

ALGOL W

<lang algolw>begin

   % Algol W only supplies sin, cos and arctan as standard. We can define    %
   % arcsin, arccos and tan functions using these. The standard functions    %
   % use radians so we also provide versions that use degrees                %

   % convert degrees to radians   %
   real procedure toRadians( real value x ) ; pi * ( x / 180 );
   % convert radians to degrees   %
   real procedure toDegrees( real value x ) ; 180 * ( x / pi );
   % tan of an angle in radians   %
   real procedure tan( real value x ) ; sin( x ) / cos( x );
   % arcsin in radians            %
   real procedure arcsin( real value x ) ; arctan( x / sqrt( 1 - ( x * x ) ) );
   % arccos in radians            %
   real procedure arccos( real value x ) ; arctan( sqrt( 1 - ( x * x ) ) / x );
   % sin of an angle in degrees   %
   real procedure sinD( real value x ) ; sin( toRadians( x ) );
   % cos of an angle in degrees   %
   real procedure cosD( real value x ) ; cos( toRadians( x ) );
   % tan of an angle in degrees   %
   real procedure tanD( real value x ) ; tan( toRadians( x ) );
   % arctan in degrees            %
   real procedure arctanD( real value x ) ; toDegrees( arctan( x ) );
   % arcsin in degrees            %
   real procedure arcsinD( real value x ) ; toDegrees( arcsin( x ) );
   % arccos in degrees            %
   real procedure arccosD( real value x ) ; toDegrees( arccos( x ) );

   % test the procedures %
   begin

       real piOver4, piOver3, oneOverRoot2, root3Over2;
       piOver3 := pi / 3; piOver4  := pi / 4;
       oneOverRoot2 := 1.0 / sqrt( 2 ); root3Over2 := sqrt( 3 ) / 2;

       r_w := 12; r_d := 5; r_format := "A"; s_w := 0; % set output format   %

       write( "PI/4: ", piOver4, " 1/root(2): ", oneOverRoot2 );
       write();
       write( "sin 45 degrees: ", sinD( 45 ), " sin pi/4 radians: ", sin( piOver4 ) );
       write( "cos 45 degrees: ", cosD( 45 ), " cos pi/4 radians: ", cos( piOver4 ) );
       write( "tan 45 degrees: ", tanD( 45 ), " tan pi/4 radians: ", tan( piOver4 ) );
       write();
       write( "arcsin( sin( pi/4 radians ) ): ", arcsin( sin( piOver4 ) ) );
       write( "arccos( cos( pi/4 radians ) ): ", arccos( cos( piOver4 ) ) );
       write( "arctan( tan( pi/4 radians ) ): ", arctan( tan( piOver4 ) ) );
       write();
       write( "PI/3: ", piOver4, " root(3)/2: ", root3Over2 );
       write();
       write( "sin 60 degrees: ", sinD( 60 ), " sin pi/3 radians: ", sin( piOver3 ) );
       write( "cos 60 degrees: ", cosD( 60 ), " cos pi/3 radians: ", cos( piOver3 ) );
       write( "tan 60 degrees: ", tanD( 60 ), " tan pi/3 radians: ", tan( piOver3 ) );
       write();
       write( "arcsin( sin( 60 degrees ) ): ", arcsinD( sinD( 60 ) ) );
       write( "arccos( cos( 60 degrees ) ): ", arccosD( cosD( 60 ) ) );
       write( "arctan( tan( 60 degrees ) ): ", arctanD( tanD( 60 ) ) );

end

end.</lang>

Output:

PI/4:      0.78539 1/root(2):      0.70710

sin 45 degrees:      0.70710 sin pi/4 radians:      0.70710
cos 45 degrees:      0.70710 cos pi/4 radians:      0.70710
tan 45 degrees:      1.00000 tan pi/4 radians:      1.00000

arcsin( sin( pi/4 radians ) ):      0.78539
arccos( cos( pi/4 radians ) ):      0.78539
arctan( tan( pi/4 radians ) ):      0.78539

PI/3:      0.78539 root(3)/2:      0.86602

sin 60 degrees:      0.86602 sin pi/3 radians:      0.86602
cos 60 degrees:      0.50000 cos pi/3 radians:      0.50000
tan 60 degrees:      1.73205 tan pi/3 radians:      1.73205

arcsin( sin( 60 degrees ) ):     60.00000
arccos( cos( 60 degrees ) ):     60.00000
arctan( tan( 60 degrees ) ):     60.00000

AutoHotkey

Translation of: C

<lang AutoHotkey>pi := 4 * atan(1)

 radians := pi / 4 
 degrees := 45.0 
 result .= "`n" . sin(radians) . "     " . sin(degrees * pi / 180)
 result .= "`n" . cos(radians) . "     " . cos(degrees * pi / 180)
 result .= "`n" . tan(radians) . "     " . tan(degrees * pi / 180)

 temp := asin(sin(radians)) 
 result .= "`n" . temp . "     " . temp * 180 / pi

 temp := acos(cos(radians)) 
 result .= "`n" . temp . "     " . temp * 180 / pi

 temp := atan(tan(radians)) 
 result .= "`n" . temp . "     " . temp * 180 / pi

msgbox % result /* output

trig.ahk

0.707107 0.707107 0.707107 0.707107 1.000000 1.000000 0.785398 45.000000 0.785398 45.000000 0.785398 45.000000

/</lang>

AWK

Awk only provides sin(), cos() and atan2(), the three bare necessities for trigonometry. They all use radians. To calculate the other functions, we use these three trigonometric identities:

tangent	arcsine	arccosine
$\tan \theta ={\frac {\sin \theta }{\cos \theta }}$	$\tan(\arcsin y)={\frac {y}{\sqrt {1-y^{2}}}}$	$\tan(\arccos x)={\frac {\sqrt {1-x^{2}}}{x}}$

With the magic of atan2(), arcsine of y is just atan2(y, sqrt(1 - y * y)), and arccosine of x is just atan2(sqrt(1 - x * x), x). This magic handles the angles arcsin(-1), arcsin 1 and arccos 0 that have no tangent. This magic also picks the angle in the correct range, so arccos(-1/2) is 2*pi/3 and not some wrong answer like -pi/3 (though tan(2*pi/3) = tan(-pi/3) = -sqrt(3).)

atan2(y, x) actually computes the angle of the point (x, y), in the range [-pi, pi]. When x > 0, this angle is the principle arctangent of y/x, in the range (-pi/2, pi/2). The calculations for arcsine and arccosine use points on the unit circle at x² + y² = 1. To calculate arcsine in the range [-pi/2, pi/2], we take the angle of points on the half-circle x = sqrt(1 - y²). To calculate arccosine in the range [0, pi], we take the angle of points on the half-circle y = sqrt(1 - x²).

<lang awk># tan(x) = tangent of x function tan(x) { return sin(x) / cos(x) }

asin(y) = arcsine of y, domain [-1, 1], range [-pi/2, pi/2]

function asin(y) { return atan2(y, sqrt(1 - y * y)) }

acos(x) = arccosine of x, domain [-1, 1], range [0, pi]

function acos(x) { return atan2(sqrt(1 - x * x), x) }

atan(y) = arctangent of y, range (-pi/2, pi/2)

function atan(y) { return atan2(y, 1) }

BEGIN { pi = atan2(0, -1) degrees = pi / 180

print "Using radians:" print " sin(-pi / 6) =", sin(-pi / 6) print " cos(3 * pi / 4) =", cos(3 * pi / 4) print " tan(pi / 3) =", tan(pi / 3) print " asin(-1 / 2) =", asin(-1 / 2) print " acos(-sqrt(2) / 2) =", acos(-sqrt(2) / 2) print " atan(sqrt(3)) =", atan(sqrt(3))

print "Using degrees:" print " sin(-30) =", sin(-30 * degrees) print " cos(135) =", cos(135 * degrees) print " tan(60) =", tan(60 * degrees) print " asin(-1 / 2) =", asin(-1 / 2) / degrees print " acos(-sqrt(2) / 2) =", acos(-sqrt(2) / 2) / degrees print " atan(sqrt(3)) =", atan(sqrt(3)) / degrees }</lang>

Output:

Using radians:
  sin(-pi / 6) = -0.5
  cos(3 * pi / 4) = -0.707107
  tan(pi / 3) = 1.73205
  asin(-1 / 2) = -0.523599
  acos(-sqrt(2) / 2) = 2.35619
  atan(sqrt(3)) = 1.0472
Using degrees:
  sin(-30) = -0.5
  cos(135) = -0.707107
  tan(60) = 1.73205
  asin(-1 / 2) = -30
  acos(-sqrt(2) / 2) = 135
  atan(sqrt(3)) = 60

Axe

Axe implements sine, cosine, and inverse tangent natively. One period is [0, 256) and the results are [-127, 127] for maximum precision.

The inverse tangent takes dX and dY parameters, rather than a single argument. This is because it is most often used to calculate angles.

Output:

  113
   68
   32

Below is the worked out math.

On a period of 256, an argument of 43 is equivalent to ${\frac {\pi }{3}}*{\frac {128}{\pi }}$ .

Furthermore, $127*{\frac {\sqrt {3}}{2}}\approx 111$ and $127*{\frac {1}{2}}\approx 64$ .

So $\sin {43}\approx 113$ and $\cos {43}\approx 68$ . Axe uses approximations to calculate the trigonometric functions.

dX and dY values of 10 mean that the angle between them should be ${\frac {\pi }{4}}$ . Indeed, the result $\tan ^{-1}{(10,10)}=32={\frac {128}{4}}$ .

BASIC

Works with: QuickBasic version 4.5

QuickBasic 4.5 does not have arcsin and arccos built in. They are defined by identities found here. <lang qbasic>pi = 3.141592653589793# radians = pi / 4 'a.k.a. 45 degrees degrees = 45 * pi / 180 'convert 45 degrees to radians once PRINT SIN(radians) + " " + SIN(degrees) 'sine PRINT COS(radians) + " " + COS(degrees) 'cosine PRINT TAN(radians) + " " + TAN (degrees) 'tangent 'arcsin thesin = SIN(radians) arcsin = ATN(thesin / SQR(1 - thesin ^ 2)) PRINT arcsin + " " + arcsin * 180 / pi 'arccos thecos = COS(radians) arccos = 2 * ATN(SQR(1 - thecos ^ 2) / (1 + thecos)) PRINT arccos + " " + arccos * 180 / pi PRINT ATN(TAN(radians)) + " " + ATN(TAN(radians)) * 180 / pi 'arctan</lang>

BBC BASIC

<lang bbcbasic> @% = &90F : REM set column width

     angle_radians = PI/5
     angle_degrees = 36
     
     PRINT SIN(angle_radians), SIN(RAD(angle_degrees))
     PRINT COS(angle_radians), COS(RAD(angle_degrees))
     PRINT TAN(angle_radians), TAN(RAD(angle_degrees))
     
     number = 0.6
     
     PRINT ASN(number), DEG(ASN(number))
     PRINT ACS(number), DEG(ACS(number))
     PRINT ATN(number), DEG(ATN(number))</lang>

bc

Library: bc -l

Translation of: AWK

<lang bc>/* t(x) = tangent of x */ define t(x) { return s(x) / c(x) }

/* y(y) = arcsine of y, domain [-1, 1], range [-pi/2, pi/2] */ define y(y) { /* Handle angles with no tangent. */ if (y == -1) return -2 * a(1) /* -pi/2 */ if (y == 1) return 2 * a(1) /* pi/2 */

/* Tangent of angle is y / x, where x^2 + y^2 = 1. */ return a(y / sqrt(1 - y * y)) }

/* x(x) = arccosine of x, domain [-1, 1], range [0, pi] */ define x(x) { auto a

/* Handle angle with no tangent. */ if (x == 0) return 2 * a(1) /* pi/2 */

/* Tangent of angle is y / x, where x^2 + y^2 = 1. */ a = a(sqrt(1 - x * x) / x) if (a < 0) { return a + 4 * a(1) /* add pi */ } else { return a } }

scale = 50 p = 4 * a(1) /* pi */ d = p / 180 /* one degree in radians */

"Using radians: " " sin(-pi / 6) = "; s(-p / 6) " cos(3 * pi / 4) = "; c(3 * p / 4) " tan(pi / 3) = "; t(p / 3) " asin(-1 / 2) = "; y(-1 / 2) " acos(-sqrt(2) / 2) = "; x(-sqrt(2) / 2) " atan(sqrt(3)) = "; a(sqrt(3))

"Using degrees: " " sin(-30) = "; s(-30 * d) " cos(135) = "; c(135 * d) " tan(60) = "; t(60 * d) " asin(-1 / 2) = "; y(-1 / 2) / d " acos(-sqrt(2) / 2) = "; x(-sqrt(2) / 2) / d " atan(sqrt(3)) = "; a(sqrt(3)) / d

quit</lang>

Output:

Using radians:
  sin(-pi / 6) = -.49999999999999999999999999999999999999999999999999
  cos(3 * pi / 4) = -.70710678118654752440084436210484903928483593768845
  tan(pi / 3) = 1.73205080756887729352744634150587236694280525381032
  asin(-1 / 2) = -.52359877559829887307710723054658381403286156656251
  acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953131
  atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312503
Using degrees:
  sin(-30) = -.49999999999999999999999999999999999999999999999981
  cos(135) = -.70710678118654752440084436210484903928483593768778
  tan(60) = 1.73205080756887729352744634150587236694280525380865
  asin(-1 / 2) = -30.00000000000000000000000000000000000000000000001203
  acos(-sqrt(2) / 2) = 135.00000000000000000000000000000000000000000000005500
  atan(sqrt(3)) = 60.00000000000000000000000000000000000000000000002463

C

<lang c>#include <math.h>

include <stdio.h>

int main() {

 double pi = 4 * atan(1);
 /*Pi / 4 is 45 degrees. All answers should be the same.*/
 double radians = pi / 4;
 double degrees = 45.0;
 double temp;
 /*sine*/
 printf("%f %f\n", sin(radians), sin(degrees * pi / 180));
 /*cosine*/
 printf("%f %f\n", cos(radians), cos(degrees * pi / 180));
 /*tangent*/
 printf("%f %f\n", tan(radians), tan(degrees * pi / 180));
 /*arcsine*/
 temp = asin(sin(radians));
 printf("%f %f\n", temp, temp * 180 / pi);
 /*arccosine*/
 temp = acos(cos(radians));
 printf("%f %f\n", temp, temp * 180 / pi);
 /*arctangent*/
 temp = atan(tan(radians));
 printf("%f %f\n", temp, temp * 180 / pi);

 return 0;

}</lang>

Output:

0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45.000000
0.785398 45.000000
0.785398 45.000000

C++

<lang cpp>#include <iostream>

include <cmath>

ifdef M_PI // defined by all POSIX systems and some non-POSIX ones

double const pi = M_PI;

else

double const pi = 4*std::atan(1);

endif

double const degree = pi/180;

int main() {

 std::cout << "=== radians ===\n";
 std::cout << "sin(pi/3) = " << std::sin(pi/3) << "\n";
 std::cout << "cos(pi/3) = " << std::cos(pi/3) << "\n";
 std::cout << "tan(pi/3) = " << std::tan(pi/3) << "\n";
 std::cout << "arcsin(1/2) = " << std::asin(0.5) << "\n";
 std::cout << "arccos(1/2) = " << std::acos(0.5) << "\n";
 std::cout << "arctan(1/2) = " << std::atan(0.5) << "\n";

 std::cout << "\n=== degrees ===\n";
 std::cout << "sin(60°) = " << std::sin(60*degree) << "\n";
 std::cout << "cos(60°) = " << std::cos(60*degree) << "\n";
 std::cout << "tan(60°) = " << std::tan(60*degree) << "\n";
 std::cout << "arcsin(1/2) = " << std::asin(0.5)/degree << "°\n";
 std::cout << "arccos(1/2) = " << std::acos(0.5)/degree << "°\n";
 std::cout << "arctan(1/2) = " << std::atan(0.5)/degree << "°\n";

 return 0;

}</lang>

C#

<lang csharp>using System;

namespace RosettaCode {

   class Program {
       static void Main(string[] args) {
           Console.WriteLine("=== radians ===");
           Console.WriteLine("sin (pi/3) = {0}", Math.Sin(Math.PI / 3));
           Console.WriteLine("cos (pi/3) = {0}", Math.Cos(Math.PI / 3));
           Console.WriteLine("tan (pi/3) = {0}", Math.Tan(Math.PI / 3));
           Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5));
           Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5));
           Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5));
           Console.WriteLine("");
           Console.WriteLine("=== degrees ===");
           Console.WriteLine("sin (60) = {0}", Math.Sin(60 * Math.PI / 180));
           Console.WriteLine("cos (60) = {0}", Math.Cos(60 * Math.PI / 180));
           Console.WriteLine("tan (60) = {0}", Math.Tan(60 * Math.PI / 180));
           Console.WriteLine("arcsin (1/2) = {0}", Math.Asin(0.5) * 180/ Math.PI);
           Console.WriteLine("arccos (1/2) = {0}", Math.Acos(0.5) * 180 / Math.PI);
           Console.WriteLine("arctan (1/2) = {0}", Math.Atan(0.5) * 180 / Math.PI);

           Console.ReadLine();
       }
   }

}</lang>

Clojure

Translation of: fortran

<lang lisp>(ns user

 (:require [clojure.contrib.generic.math-functions :as generic]))

(def pi Math/PI)

(def pi (* 4 (atan 1))) (def dtor (/ pi 180)) (def rtod (/ 180 pi)) (def radians (/ pi 4)) (def degrees 45)

(println (str (sin radians) " " (sin (* degrees dtor)))) (println (str (cos radians) " " (cos (* degrees dtor)))) (println (str (tan radians) " " (tan (* degrees dtor)))) (println (str (asin (sin radians) ) " " (* (asin (sin (* degrees dtor))) rtod))) (println (str (acos (cos radians) ) " " (* (acos (cos (* degrees dtor))) rtod))) (println (str (atan (tan radians) ) " " (* (atan (tan (* degrees dtor))) rtod)))</lang>

Output:

(matches that of Java)

0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

COBOL

<lang cobol> IDENTIFICATION DIVISION.

      PROGRAM-ID. Trig.

      DATA DIVISION.
      WORKING-STORAGE SECTION.
      01  Pi-Third   USAGE COMP-2.
      01  Degree     USAGE COMP-2.

      01  60-Degrees USAGE COMP-2.

      01  Result     USAGE COMP-2.

      PROCEDURE DIVISION.
          COMPUTE Pi-Third = FUNCTION PI / 3

          DISPLAY "Radians:"
          DISPLAY "  Sin(π / 3)  = " FUNCTION SIN(Pi-Third)
          DISPLAY "  Cos(π / 3)  = " FUNCTION COS(Pi-Third)
          DISPLAY "  Tan(π / 3)  = " FUNCTION TAN(Pi-Third)
          DISPLAY "  Asin(0.5)   = " FUNCTION ASIN(0.5)
          DISPLAY "  Acos(0.5)   = " FUNCTION ACOS(0.5)
          DISPLAY "  Atan(0.5)   = " FUNCTION ATAN(0.5)

          COMPUTE Degree = FUNCTION PI / 180
          COMPUTE 60-Degrees = Degree * 60

          DISPLAY "Degrees:"
          DISPLAY "  Sin(60°)  = " FUNCTION SIN(60-Degrees)
          DISPLAY "  Cos(60°)  = " FUNCTION COS(60-Degrees)
          DISPLAY "  Tan(60°)  = " FUNCTION TAN(60-Degrees)
          COMPUTE Result = FUNCTION ASIN(0.5) / 60
          DISPLAY "  Asin(0.5) = " Result
          COMPUTE Result = FUNCTION ACOS(0.5) / 60
          DISPLAY "  Acos(0.5) = " Result
          COMPUTE Result = FUNCTION ATAN(0.5) / 60
          DISPLAY "  Atan(0.5) = " Result

          GOBACK
          .</lang>

Output:

Radians:
  Sin(π / 3)  = +0.86602540368613976
  Cos(π / 3)  = +0.50000000017025856
  Tan(π / 3)  = 1.732050806782486241
  Asin(0.5) = +0.52359877559829897
  Acos(0.5) = 1.04719755119659785
  Atan(0.5) = +0.52359877559829897
Degrees:
  Sin(60°)  = +0.86602538768613932
  Cos(60°)  = +0.50000002788307131
  Tan(60°)  = 1.732050678782493636
  Asin(0.5) = 0.008726645999999999
  Acos(0.5) = 0.017453291999999999
  Atan(0.5) = 0.007727460000000000

Common Lisp

<lang lisp>(defun deg->rad (x) (* x (/ pi 180))) (defun rad->deg (x) (* x (/ 180 pi)))

(mapc (lambda (x) (format t "~s => ~s~%" x (eval x)))

 '((sin (/ pi 4))
   (sin (deg->rad 45))
   (cos (/ pi 6))
   (cos (deg->rad 30))
   (tan (/ pi 3))
   (tan (deg->rad 60))
   (asin 1)
   (rad->deg (asin 1))
   (acos 1/2)
   (rad->deg (acos 1/2))
   (atan 15)
   (rad->deg (atan 15))))</lang>

D

Translation of: C

<lang d>void main() {

   import std.stdio, std.math;

   enum degrees = 45.0L;
   enum t0 = degrees * PI / 180.0L;
   writeln("Reference:  0.7071067811865475244008");
   writefln("Sine:       %.20f  %.20f", PI_4.sin, t0.sin);
   writefln("Cosine:     %.20f  %.20f", PI_4.cos, t0.cos);
   writefln("Tangent:    %.20f  %.20f", PI_4.tan, t0.tan);

   writeln;
   writeln("Reference:  0.7853981633974483096156");
   immutable real t1 = PI_4.sin.asin;
   writefln("Arcsine:    %.20f %.20f", t1, t1 * 180.0L / PI);

   immutable real t2 = PI_4.cos.acos;
   writefln("Arccosine:  %.20f %.20f", t2, t2 * 180.0L / PI);

   immutable real t3 = PI_4.tan.atan;
   writefln("Arctangent: %.20f %.20f", t3, t3 * 180.0L / PI);

}</lang>

Output:

Reference:  0.7071067811865475244008
Sine:       0.70710678118654752442  0.70710678118654752442
Cosine:     0.70710678118654752438  0.70710678118654752438
Tangent:    1.00000000000000000000  1.00000000000000000000

Reference:  0.7853981633974483096156
Arcsine:    0.78539816339744830970 45.00000000000000000400
Arccosine:  0.78539816339744830961 45.00000000000000000000
Arctangent: 0.78539816339744830961 45.00000000000000000000

E

Translation of: ALGOL 68

<lang e>def pi := (-1.0).acos()

def radians := pi / 4.0 def degrees := 45.0

def d2r := (pi/180).multiply def r2d := (180/pi).multiply

println(`$\ ${radians.sin()} ${d2r(degrees).sin()} ${radians.cos()} ${d2r(degrees).cos()} ${radians.tan()} ${d2r(degrees).tan()} ${def asin := radians.sin().asin()} ${r2d(asin)} ${def acos := radians.cos().acos()} ${r2d(acos)} ${def atan := radians.tan().atan()} ${r2d(atan)} `)</lang>

Output:

0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

Elena

Translation of: C

import system.
import system'math.

symbol program =

[

   console writeLine:"Radians:".
   console writeLine:("sin(π/3) = " + ((pi_value/3) sin) literal).
   console writeLine:("cos(π/3) = " + ((pi_value/3) cos) literal).
   console writeLine:("tan(π/3) = " + ((pi_value/3) tan) literal).
   console writeLine:("arcsin(1/2) = " + (0.5r arcsin literal)).
   console writeLine:("arccos(1/2) = " + (0.5r arccos literal)).
   console writeLine:("arctan(1/2) = " + (0.5r arctan literal)).
   console writeLine:"".
   
   console writeLine:"Degrees:".
   console writeLine:("sin(60º) = " + ((60.0r radian) sin) literal).
   console writeLine:("cos(60º) = " + ((60.0r radian) cos) literal).
   console writeLine:("tan(60º) = " + ((60.0r radian) tan) literal).
   console writeLine:("arcsin(1/2) = " + ((0.5r arcsin) degree) literal + "º").
   console writeLine:("arccos(1/2) = " + ((0.5r arccos) degree) literal + "º").
   console writeLine:("arctan(1/2) = " + ((0.5r arctan) degree) literal + "º").

]. </lang>

Elixir

Translation of: Erlang

Erlang

Translation of: C

<lang erlang> Deg=45. Rad=math:pi()/4.

math:sin(Deg * math:pi() / 180)==math:sin(Rad). </lang>

Output:

true

Output:

true

Output:

true

Output:

true

Output:

true

Fantom

Fantom's Float library includes all six trigonometric functions, which assume the number is in radians.
Methods are provided to convert: toDegrees and toRadians.

<lang fantom> class Main {

 public static Void main ()
 {
   Float r := Float.pi / 4
   echo (r.sin)
   echo (r.cos)
   echo (r.tan)
   echo (r.asin)
   echo (r.acos)
   echo (r.atan)
   // and from degrees
   echo (45.0f.toRadians.sin)
   echo (45.0f.toRadians.cos)
   echo (45.0f.toRadians.tan)
   echo (45.0f.toRadians.asin)
   echo (45.0f.toRadians.acos)
   echo (45.0f.toRadians.atan)
 }

} </lang>

Forth

<lang forth>45e pi f* 180e f/ \ radians

cr fdup fsin f. \ also available: fsincos ( r -- sin cos ) cr fdup fcos f. cr fdup ftan f. cr fdup fasin f. cr fdup facos f. cr fatan f. \ also available: fatan2 ( r1 r2 -- atan[r1/r2] )</lang>

Fortran

Trigonometic functions expect arguments in radians so degrees require conversion <lang fortran>PROGRAM Trig

 REAL pi, dtor, rtod, radians, degrees

 pi = 4.0 * ATAN(1.0)
 dtor = pi / 180.0
 rtod = 180.0 / pi
 radians = pi / 4.0
 degrees = 45.0 

 WRITE(*,*) SIN(radians), SIN(degrees*dtor)
 WRITE(*,*) COS(radians), COS(degrees*dtor)
 WRITE(*,*) TAN(radians), TAN(degrees*dtor)
 WRITE(*,*) ASIN(SIN(radians)), ASIN(SIN(degrees*dtor))*rtod
 WRITE(*,*) ACOS(COS(radians)), ACOS(COS(degrees*dtor))*rtod
 WRITE(*,*) ATAN(TAN(radians)), ATAN(TAN(degrees*dtor))*rtod

END PROGRAM Trig</lang>

Output:

 0.707107   0.707107
 0.707107   0.707107
  1.00000    1.00000
 0.785398    45.0000
 0.785398    45.0000
 0.785398    45.0000

The following trigonometric functions are also available <lang fortran>ATAN2(y,x) ! Arctangent(y/x), -pi < result <= +pi SINH(x) ! Hyperbolic sine COSH(x) ! Hyperbolic cosine TANH(x) ! Hyperbolic tangent</lang>

But, for those with access to fatter Fortran function libraries, trigonometrical functions working in degrees are also available. <lang Fortran> Calculate various trigonometric functions from the Fortran library.

     INTEGER BIT(32),B,IP	!Stuff for bit fiddling.
     INTEGER ENUFF,I		!Step through the test angles.
     PARAMETER (ENUFF = 17)	!A selection of special values.
     INTEGER ANGLE(ENUFF)	!All in whole degrees.
     DATA ANGLE/0,30,45,60,90,120,135,150,180,	!Here they are.
    1 210,225,240,270,300,315,330,360/		!Thus check angle folding.
     REAL PI,DEG2RAD		!Special numbers.
     REAL D,R,FD,FR,AD,AR	!Degree, Radian, F(D), F(R), inverses.
     PI = 4*ATAN(1.0)		!SINGLE PRECISION 1·0.
     DEG2RAD = PI/180		!Limited precision here too for a transcendental number.

Case the first: sines.

     WRITE (6,10) ("Sin", I = 1,4)	!Supply some names.
  10 FORMAT (" Deg.",A7,"(Deg)",A7,"(Rad)   Rad - Deg",	!Ah, layout.
    1 6X,"Arc",A3,"D",6X,"Arc",A3,"R",9X,"Diff")
     DO I = 1,ENUFF		!Step through the test values.
       D = ANGLE(I)			!The angle in degrees, in floating point.
       R = D*DEG2RAD			!Approximation, in radians.
       FD = SIND(D); AD = ASIND(FD)		!Functions working in degrees.
       FR = SIN(R);  AR = ASIN(FR)/DEG2RAD	!Functions working in radians.
       WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD	!Results.
  11   FORMAT (I4,":",3F12.8,3F13.7)	!Ah, alignment with FORMAT 10...
     END DO			!On to the next test value.

Case the second: cosines.

     WRITE (6,10) ("Cos", I = 1,4)
     DO I = 1,ENUFF
       D = ANGLE(I)
       R = D*DEG2RAD
       FD = COSD(D); AD = ACOSD(FD)
       FR = COS(R);  AR = ACOS(FR)/DEG2RAD
       WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD
     END DO

Case the third: tangents.

     WRITE (6,10) ("Tan", I = 1,4)
     DO I = 1,ENUFF
       D = ANGLE(I)
       R = D*DEG2RAD
       FD = TAND(D); AD = ATAND(FD)
       FR = TAN(R);  AR = ATAN(FR)/DEG2RAD
       WRITE (6,11) INT(D),FD,FR,FR - FD,AD,AR,AR - AD
     END DO
     WRITE (6,*) "...Special deal for 90 degrees..."
     D = 90
     R = D*DEG2RAD
     FD = TAND(D); AD = ATAND(FD)
     FR = TAN(R);  AR = ATAN(FR)/DEG2RAD
     WRITE (6,*) "TanD =",FD,"Atan =",AD
     WRITE (6,*) "TanR =",FR,"Atan =",AR

Convert PI to binary...

     PI = PI - 3	!I know it starts with three, and I need the fractional part.
     BIT(1:2) = 1	!So, the binary is 11. something.
     B = 2		!Two bits known.
     DO I = 1,26	!For single precision, more than enough additional bits.
       PI = PI*2		!Hoist a bit to the hot spot.
       IP = PI			!The integral part.
       PI = PI - IP		!Remove it from the work in progress.
       B = B + 1		!Another bit bitten.
       BIT(B) = IP		!Place it.
     END DO		!On to the next.
     WRITE (6,20) BIT(1:B)	!Reveal the bits.
  20 FORMAT (" Pi ~ ",2I1,".",66I1)	!A known format.
     WRITE (6,*) "   = 11.00100100001111110110101010001000100001..."	!But actually...
     END		!So much for that.

</lang> Output:

Deg.    Sin(Deg)    Sin(Rad)   Rad - Deg      ArcSinD      ArcSinR         Diff
  0:  0.00000000  0.00000000  0.00000000    0.0000000    0.0000000    0.0000000
 30:  0.50000000  0.50000000  0.00000000   30.0000000   30.0000000    0.0000000
 45:  0.70710677  0.70710677  0.00000000   45.0000000   45.0000000    0.0000000
 60:  0.86602539  0.86602545  0.00000006   60.0000000   60.0000038    0.0000038
 90:  1.00000000  1.00000000  0.00000000   90.0000000   90.0000000    0.0000000
120:  0.86602539  0.86602539  0.00000000   60.0000000   60.0000000    0.0000000
135:  0.70710677  0.70710677  0.00000000   45.0000000   45.0000000    0.0000000
150:  0.50000000  0.50000006  0.00000006   30.0000000   30.0000038    0.0000038
180:  0.00000000 -0.00000009 -0.00000009    0.0000000   -0.0000050   -0.0000050
210: -0.50000000 -0.49999997  0.00000003  -30.0000000  -29.9999981    0.0000019
225: -0.70710677 -0.70710671  0.00000006  -45.0000000  -44.9999962    0.0000038
240: -0.86602539 -0.86602545 -0.00000006  -60.0000000  -60.0000038   -0.0000038
270: -1.00000000 -1.00000000  0.00000000  -90.0000000  -90.0000000    0.0000000
300: -0.86602539 -0.86602545 -0.00000006  -60.0000000  -60.0000038   -0.0000038
315: -0.70710677 -0.70710689 -0.00000012  -45.0000000  -45.0000076   -0.0000076
330: -0.50000000 -0.50000018 -0.00000018  -30.0000000  -30.0000114   -0.0000114
360:  0.00000000  0.00000017  0.00000017    0.0000000    0.0000100    0.0000100
Deg.    Cos(Deg)    Cos(Rad)   Rad - Deg      ArcCosD      ArcCosR         Diff
  0:  1.00000000  1.00000000  0.00000000    0.0000000    0.0000000    0.0000000
 30:  0.86602539  0.86602539  0.00000000   30.0000019   30.0000019    0.0000000
 45:  0.70710677  0.70710677  0.00000000   45.0000000   45.0000000    0.0000000
 60:  0.50000000  0.49999997 -0.00000003   60.0000000   60.0000038    0.0000038
 90:  0.00000000 -0.00000004 -0.00000004   90.0000000   90.0000000    0.0000000
120: -0.50000000 -0.50000006 -0.00000006  120.0000000  120.0000076    0.0000076
135: -0.70710677 -0.70710677  0.00000000  135.0000000  135.0000000    0.0000000
150: -0.86602539 -0.86602539  0.00000000  150.0000000  150.0000000    0.0000000
180: -1.00000000 -1.00000000  0.00000000  180.0000000  180.0000000    0.0000000
210: -0.86602539 -0.86602539  0.00000000  150.0000000  150.0000000    0.0000000
225: -0.70710677 -0.70710683 -0.00000006  135.0000000  135.0000000    0.0000000
240: -0.50000000 -0.49999991  0.00000009  120.0000000  119.9999924   -0.0000076
270:  0.00000000  0.00000001  0.00000001   90.0000000   90.0000000    0.0000000
300:  0.50000000  0.49999991 -0.00000009   60.0000000   60.0000076    0.0000076
315:  0.70710677  0.70710665 -0.00000012   45.0000000   45.0000114    0.0000114
330:  0.86602539  0.86602533 -0.00000006   30.0000019   30.0000095    0.0000076
360:  1.00000000  1.00000000  0.00000000    0.0000000    0.0000000    0.0000000
Deg.    Tan(Deg)    Tan(Rad)   Rad - Deg      ArcTanD      ArcTanR         Diff
  0:  0.00000000  0.00000000  0.00000000    0.0000000    0.0000000    0.0000000
 30:  0.57735026  0.57735026  0.00000000   30.0000000   30.0000000    0.0000000
 45:  1.00000000  1.00000000  0.00000000   45.0000000   45.0000000    0.0000000
 60:  1.73205078  1.73205090  0.00000012   60.0000000   60.0000000    0.0000000
 90:************************************   90.0000000  -90.0000000 -180.0000000
120: -1.73205078 -1.73205054  0.00000024  -60.0000000  -59.9999962    0.0000038
135: -1.00000000 -1.00000000  0.00000000  -45.0000000  -45.0000000    0.0000000
150: -0.57735026 -0.57735032 -0.00000006  -30.0000000  -30.0000019   -0.0000019
180:  0.00000000  0.00000009  0.00000009    0.0000000    0.0000050    0.0000050
210:  0.57735026  0.57735026  0.00000000   30.0000000   30.0000000    0.0000000
225:  1.00000000  0.99999988 -0.00000012   45.0000000   44.9999962   -0.0000038
240:  1.73205078  1.73205125  0.00000048   60.0000000   60.0000076    0.0000076
270:************************************   90.0000000  -90.0000000 -180.0000000
300: -1.73205078 -1.73205113 -0.00000036  -60.0000000  -60.0000038   -0.0000038
315: -1.00000000 -1.00000024 -0.00000024  -45.0000000  -45.0000076   -0.0000076
330: -0.57735026 -0.57735056 -0.00000030  -30.0000000  -30.0000134   -0.0000134
360:  0.00000000  0.00000017  0.00000017    0.0000000    0.0000100    0.0000100
...Special deal for 90 degrees...
TanD =  1.6331778E+16 Atan =   90.00000    
TanR = -2.2877332E+07 Atan =  -90.00000    
Pi ~ 11.00100100001111110110110000
   = 11.00100100001111110110101010001000100001...

Notice that the calculations in radians are less accurate. Firstly, pi cannot be represented exactly and secondly, the conversion factor of pi/180 or 180/pi adds further to the error. The degree-based functions obviously can fold their angles using exact arithmetic (though ACosD has surprising trouble with 30°) and so 360° is the same as 0°, unlike the case with radians. TanD(90°) should yield Infinity (but, which sign?) but perhaps this latter-day feature of computer floating-point was not included. In any case, Tan(90° in radians) faces the problem that its parameter will not in fact be pi/2 but some value just over (or under), and likewise with double precision and quadruple precision and any other finite precision.

F#

<lang fsharp>open NUnit.Framework open FsUnit

// radian

[<Test>] let ``Verify that sin pi returns 0`` () =

 let x = System.Math.Sin System.Math.PI
 System.Math.Round(x,5) |> should equal 0

[<Test>] let ``Verify that cos pi returns -1`` () =

 let x = System.Math.Cos System.Math.PI
 System.Math.Round(x,5) |> should equal -1

[<Test>] let ``Verify that tan pi returns 0`` () =

 let x = System.Math.Tan System.Math.PI
 System.Math.Round(x,5) |> should equal 0

[<Test>] let ``Verify that sin pi/2 returns 1`` () =

 let x = System.Math.Sin (System.Math.PI / 2.0)
 System.Math.Round(x,5) |> should equal 1

[<Test>] let ``Verify that cos pi/2 returns -1`` () =

 let x = System.Math.Cos (System.Math.PI / 2.0)
 System.Math.Round(x,5) |> should equal 0

[<Test>] let ``Verify that sin pi/3 returns sqrt 3/2`` () =

 let actual = System.Math.Sin (System.Math.PI / 3.0)
 let expected = System.Math.Round((System.Math.Sqrt 3.0) / 2.0, 5)
 System.Math.Round(actual,5) |> should equal expected

[<Test>] let ``Verify that cos pi/3 returns -1`` () =

 let x = System.Math.Cos (System.Math.PI / 3.0)
 System.Math.Round(x,5) |> should equal 0.5

[<Test>] let ``Verify that cos and sin of pi/4 return same value`` () =

 let c = System.Math.Cos (System.Math.PI / 4.0)
 let s = System.Math.Sin (System.Math.PI / 4.0)
 System.Math.Round(c,5) = System.Math.Round(s,5) |> should be True

[<Test>] let ``Verify that acos pi/3 returns 1/2`` () =

 let actual = System.Math.Acos 0.5
 let expected = System.Math.Round((System.Math.PI / 3.0),5)
 System.Math.Round(actual,5) |> should equal expected

[<Test>] let ``Verify that asin 1 returns pi/2`` () =

 let actual = System.Math.Asin 1.0
 let expected = System.Math.Round((System.Math.PI / 2.0),5)
 System.Math.Round(actual,5) |> should equal expected

[<Test>] let ``Verify that atan 0 returns 0`` () =

 let actual = System.Math.Atan 0.0
 let expected = System.Math.Round(0.0,5)
 System.Math.Round(actual,5) |> should equal expected

// degree

let toRadians d = d * System.Math.PI / 180.0

[<Test>] let ``Verify that pi is 180 degrees`` () =

 toRadians 180.0 |> should equal System.Math.PI

[<Test>] let ``Verify that pi/2 is 90 degrees`` () =

 toRadians 90.0 |> should equal (System.Math.PI / 2.0)

[<Test>] let ``Verify that pi/3 is 60 degrees`` () =

 toRadians 60.0 |> should equal (System.Math.PI / 3.0)

[<Test>] let ``Verify that sin 180 returns 0`` () =

 let x = System.Math.Sin (toRadians 180.0)
 System.Math.Round(x,5) |> should equal 0

[<Test>] let ``Verify that cos 180 returns -1`` () =

 let x = System.Math.Cos (toRadians 180.0)
 System.Math.Round(x,5) |> should equal -1

[<Test>] let ``Verify that tan 180 returns 0`` () =

 let x = System.Math.Tan (toRadians 180.0)
 System.Math.Round(x,5) |> should equal 0

[<Test>] let ``Verify that sin 90 returns 1`` () =

 let x = System.Math.Sin (toRadians 90.0)
 System.Math.Round(x,5) |> should equal 1

[<Test>] let ``Verify that cos 90 returns -1`` () =

 let x = System.Math.Cos (toRadians 90.0)
 System.Math.Round(x,5) |> should equal 0

[<Test>] let ``Verify that sin 60 returns sqrt 3/2`` () =

 let actual = System.Math.Sin (toRadians 60.0)
 let expected = System.Math.Round((System.Math.Sqrt 3.0) / 2.0, 5)
 System.Math.Round(actual,5) |> should equal expected

[<Test>] let ``Verify that cos 60 returns -1`` () =

 let x = System.Math.Cos (toRadians 60.0)
 System.Math.Round(x,5) |> should equal 0.5

[<Test>] let ``Verify that cos and sin of 45 return same value`` () =

 let c = System.Math.Cos (toRadians 45.0)
 let s = System.Math.Sin (toRadians 45.0)
 System.Math.Round(c,5) = System.Math.Round(s,5) |> should be True</lang>

GAP

<lang gap># GAP has an improved floating-point support since version 4.5

Pi := Acos(-1.0);

r := Pi / 5.0; d := 36;

Deg := x -> x * Pi / 180;

Sin(r); Asin(last); Sin(Deg(d)); Asin(last); Cos(r); Acos(last); Cos(Deg(d)); Acos(last); Tan(r); Atan(last); Tan(Deg(d)); Atan(last);</lang>

Go

The Go math package provides the constant pi and the six trigonometric functions called for by the task. The functions all use the float64 type and work in radians. It also provides a Sincos function. <lang go>package main

import (

   "fmt"
   "math"

)

const d = 30. const r = d * math.Pi / 180

var s = .5 var c = math.Sqrt(3) / 2 var t = 1 / math.Sqrt(3)

func main() {

   fmt.Printf("sin(%9.6f deg) = %f\n", d, math.Sin(d*math.Pi/180))
   fmt.Printf("sin(%9.6f rad) = %f\n", r, math.Sin(r))
   fmt.Printf("cos(%9.6f deg) = %f\n", d, math.Cos(d*math.Pi/180))
   fmt.Printf("cos(%9.6f rad) = %f\n", r, math.Cos(r))
   fmt.Printf("tan(%9.6f deg) = %f\n", d, math.Tan(d*math.Pi/180))
   fmt.Printf("tan(%9.6f rad) = %f\n", r, math.Tan(r))
   fmt.Printf("asin(%f) = %9.6f deg\n", s, math.Asin(s)*180/math.Pi)
   fmt.Printf("asin(%f) = %9.6f rad\n", s, math.Asin(s))
   fmt.Printf("acos(%f) = %9.6f deg\n", c, math.Acos(c)*180/math.Pi)
   fmt.Printf("acos(%f) = %9.6f rad\n", c, math.Acos(c))
   fmt.Printf("atan(%f) = %9.6f deg\n", t, math.Atan(t)*180/math.Pi)
   fmt.Printf("atan(%f) = %9.6f rad\n", t, math.Atan(t))

}</lang>

Output:

sin(30.000000 deg) = 0.500000
sin( 0.523599 rad) = 0.500000
cos(30.000000 deg) = 0.866025
cos( 0.523599 rad) = 0.866025
tan(30.000000 deg) = 0.577350
tan( 0.523599 rad) = 0.577350
asin(0.500000) = 30.000000 deg
asin(0.500000) =  0.523599 rad
acos(0.866025) = 30.000000 deg
acos(0.866025) =  0.523599 rad
atan(0.577350) = 30.000000 deg
atan(0.577350) =  0.523599 rad

Groovy

Trig functions use radians, degrees must be converted to/from radians <lang groovy>def radians = Math.PI/4 def degrees = 45

def d2r = { it*Math.PI/180 } def r2d = { it*180/Math.PI }

println "sin(\u03C0/4) = ${Math.sin(radians)} == sin(45\u00B0) = ${Math.sin(d2r(degrees))}" println "cos(\u03C0/4) = ${Math.cos(radians)} == cos(45\u00B0) = ${Math.cos(d2r(degrees))}" println "tan(\u03C0/4) = ${Math.tan(radians)} == tan(45\u00B0) = ${Math.tan(d2r(degrees))}" println "asin(\u221A2/2) = ${Math.asin(2**(-0.5))} == asin(\u221A2/2)\u00B0 = ${r2d(Math.asin(2**(-0.5)))}\u00B0" println "acos(\u221A2/2) = ${Math.acos(2**(-0.5))} == acos(\u221A2/2)\u00B0 = ${r2d(Math.acos(2**(-0.5)))}\u00B0" println "atan(1) = ${Math.atan(1)} == atan(1)\u00B0 = ${r2d(Math.atan(1))}\u00B0"</lang>

Output:

sin(π/4) = 0.7071067811865475  == sin(45°) = 0.7071067811865475
cos(π/4) = 0.7071067811865476  == cos(45°) = 0.7071067811865476
tan(π/4) = 0.9999999999999999  == tan(45°) = 0.9999999999999999
asin(√2/2) = 0.7853981633974482 == asin(√2/2)° = 44.99999999999999°
acos(√2/2) = 0.7853981633974484 == acos(√2/2)° = 45.00000000000001°
atan(1) = 0.7853981633974483 == atan(1)° = 45.0°

Haskell

Trigonometric functions use radians; degrees require conversion.

<lang haskell>fromDegrees deg = deg * pi / 180 toDegrees rad = rad * 180 / pi

example = [

 sin (pi / 6), sin (fromDegrees 30), 
 cos (pi / 6), cos (fromDegrees 30), 
 tan (pi / 6), tan (fromDegrees 30), 
 asin 0.5, toDegrees (asin 0.5),
 acos 0.5, toDegrees (acos 0.5),
 atan 0.5, toDegrees (atan 0.5)]</lang>

HicEst

Translated from Fortran: <lang hicest>pi = 4.0 * ATAN(1.0) dtor = pi / 180.0 rtod = 180.0 / pi radians = pi / 4.0 degrees = 45.0

WRITE(ClipBoard) SIN(radians), SIN(degrees*dtor) WRITE(ClipBoard) COS(radians), COS(degrees*dtor) WRITE(ClipBoard) TAN(radians), TAN(degrees*dtor) WRITE(ClipBoard) ASIN(SIN(radians)), ASIN(SIN(degrees*dtor))*rtod WRITE(ClipBoard) ACOS(COS(radians)), ACOS(COS(degrees*dtor))*rtod WRITE(ClipBoard) ATAN(TAN(radians)), ATAN(TAN(degrees*dtor))*rtod</lang> <lang hicest>0.7071067812 0.7071067812 0.7071067812 0.7071067812 1 1 0.7853981634 45 0.7853981634 45 0.7853981634 45</lang> SINH, COSH, TANH, and inverses are available as well.

IDL

<lang idl>deg = 35 ; arbitrary number of degrees rad = !dtor*deg ; system variables !dtor and !radeg convert between rad and deg</lang> <lang idl>; the trig functions receive and emit radians: print, rad, sin(rad), asin(sin(rad)) print, cos(rad), acos(cos(rad)) print, tan(rad), atan(tan(rad)) ; etc

prints the following
0.610865 0.573576 0.610865
0.819152 0.610865
0.700208 0.610865</lang>

<lang idl>; the hyperbolic versions exist and behave as expected: print, sinh(rad) ; etc

outputs
0.649572</lang>

<lang idl>;If the input is an array, the output has the same dimensions etc as the input: x = !dpi/[[2,3],[4,5],[6,7]] ; !dpi is a read-only sysvar = 3.1415... print,sin(x)

outputs
1.0000000 0.86602540
0.70710678 0.58778525
0.50000000 0.43388374</lang>

<lang idl>; the trig functions behave as expected for complex arguments: x = complex(1,2) print,sin(x)

outputs
( 3.16578, 1.95960)</lang>

Icon and Unicon

Icon and Unicon trig functions 'sin', 'cos', 'tan', 'asin', 'acos', and 'atan' operate on angles expressed in radians. Conversion functions 'dtor' and 'rtod' convert between the two systems. The example below uses string invocation to construct and call the functions:

Icon

<lang Icon>invocable all procedure main()

d := 30 # degrees r := dtor(d) # convert to radians

every write(f := !["sin","cos","tan"],"(",r,")=",y := f(r)," ",fi := "a" || f,"(",y,")=",x := fi(y)," rad = ",rtod(x)," deg") end</lang>

Output:

sin(0.5235987755982988)=0.4999999999999999 asin(0.4999999999999999)=0.5235987755982988 rad = 30.0 deg
cos(0.5235987755982988)=0.8660254037844387 acos(0.8660254037844387)=0.5235987755982987 rad = 29.99999999999999 deg
tan(0.5235987755982988)=0.5773502691896257 atan(0.5773502691896257)=0.5235987755982988 rad = 30.0 deg

Unicon

The Icon solution works in Unicon.

J

The circle functions in J include trigonometric functions. Native operation is in radians, so values in degrees involve conversion.

Sine, cosine, and tangent of a single angle, indicated as pi-over-four radians and as 45 degrees: <lang j> (1&o. , 2&o. ,: 3&o.) (4 %~ o. 1) , 180 %~ o. 45 0.707107 0.707107 0.707107 0.707107

      1        1</lang>

Arcsine, arccosine, and arctangent of one-half, in radians and degrees: <lang j> ([ ,. 180p_1&*) (_1&o. , _2&o. ,: _3&o.) 0.5 0.523599 30

 1.0472      60

0.463648 26.5651</lang>

The trig script adds cover functions for the trigonometric operations as well as verbs for converting degrees from radians (dfr) and radians from degrees (rfd) <lang j> require 'trig'

  (sin , cos ,: tan) (1p1 % 4), rfd 45

0.707107 0.707107 0.707107 0.707107

      1        1

  ([ ,. dfr) (arcsin , arccos ,: arctan) 0.5

0.523599 30

 1.0472      60

0.463648 26.5651</lang>

Java

Java's Math class contains all six functions and is automatically included as part of the language. The functions all accept radians only, so conversion is necessary when dealing with degrees. The Math class also has a PI constant for easy conversion.

<lang java>public class Trig {

       public static void main(String[] args) {
               //Pi / 4 is 45 degrees. All answers should be the same.
               double radians = Math.PI / 4;
               double degrees = 45.0;
               //sine
               System.out.println(Math.sin(radians) + " " + Math.sin(Math.toRadians(degrees)));
               //cosine
               System.out.println(Math.cos(radians) + " " + Math.cos(Math.toRadians(degrees)));
               //tangent
               System.out.println(Math.tan(radians) + " " + Math.tan(Math.toRadians(degrees)));
               //arcsine
               double arcsin = Math.asin(Math.sin(radians));
               System.out.println(arcsin + " " + Math.toDegrees(arcsin));
               //arccosine
               double arccos = Math.acos(Math.cos(radians));
               System.out.println(arccos + " " + Math.toDegrees(arccos));
               //arctangent
               double arctan = Math.atan(Math.tan(radians));
               System.out.println(arctan + " " + Math.toDegrees(arctan));
       }

}</lang>

Output:

0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

JavaScript

JavaScript's Math class contains all six functions and is automatically included as part of the language. The functions all accept radians only, so conversion is necessary when dealing with degrees. The Math class also has a PI constant for easy conversion.

<lang javascript>var

radians = Math.PI / 4, // Pi / 4 is 45 degrees. All answers should be the same.
degrees = 45.0,
sine = Math.sin(radians),
cosine = Math.cos(radians),
tangent = Math.tan(radians),
arcsin = Math.asin(sine),
arccos = Math.acos(cosine),
arctan = Math.atan(tangent);

// sine window.alert(sine + " " + Math.sin(degrees * Math.PI / 180)); // cosine window.alert(cosine + " " + Math.cos(degrees * Math.PI / 180)); // tangent window.alert(tangent + " " + Math.tan(degrees * Math.PI / 180)); // arcsine window.alert(arcsin + " " + (arcsin * 180 / Math.PI)); // arccosine window.alert(arccos + " " + (arccos * 180 / Math.PI)); // arctangent window.alert(arctan + " " + (arctan * 180 / Math.PI));</lang>

jq

jq includes the standard C-library trigonometric functions (sin, cos, tan, asin, acos, atan), but they are provided as filters as illustrated in the definition of radians below.

The trigonometric filters only accept radians, so conversion is necessary when dealing with degrees. The constant π can be defined as also shown in the following definition of radians:<lang jq>

degrees to radians

def radians:

 (-1|acos) as $pi | (. * $pi / 180);

def task:

 (-1|acos) as $pi
 |  ($pi / 180) as $degrees
 | "Using radians:",
   "  sin(-pi / 6)     = \( (-$pi / 6)    | sin )",
   "  cos(3 * pi / 4)  = \( (3 * $pi / 4) | cos)",
   "  tan(pi / 3)      = \( ($pi / 3)     | tan)",
   "  asin(-1 / 2)     = \((-1 / 2)       | asin)",
   "  acos(-sqrt(2)/2) = \((-(2|sqrt)/2)  | acos )",
   "  atan(sqrt(3))    = \(      3 | sqrt | atan )",

   "Using degrees:",
   "  sin(-30)         = \((-30 * $degrees) | sin)",
   "  cos(135)         = \((135 * $degrees) | cos)",
   "  tan(60)          = \(( 60 * $degrees) | tan)",
   "  asin(-1 / 2)     = \(        (-1 / 2) | asin / $degrees)",
   "  acos(-sqrt(2)/2) = \( (-(2|sqrt) / 2) | acos / $degrees)",
   "  atan(sqrt(3))    = \( (3 | sqrt)      | atan / $degrees)"

task </lang>

Output:

<lang sh>Using radians:

 sin(-pi / 6)     = -0.49999999999999994
 cos(3 * pi / 4)  = -0.7071067811865475
 tan(pi / 3)      = 1.7320508075688767
 asin(-1 / 2)     = -0.5235987755982988
 acos(-sqrt(2)/2) = 2.356194490192345
 atan(sqrt(3))    = 1.0471975511965979

Using degrees:

 sin(-30)         = -0.49999999999999994
 cos(135)         = -0.7071067811865475
 tan(60)          = 1.7320508075688767
 asin(-1 / 2)     = -29.999999999999996
 acos(-sqrt(2)/2) = 135
 atan(sqrt(3))    = 60.00000000000001</lang>

Liberty BASIC

<lang lb>pi = ACS(-1) radians = pi / 4.0 rtod = 180 / pi degrees = radians * rtod dtor = pi / 180

'LB works in radians, so degrees require conversion print "Sin: ";SIN(radians);" "; SIN(degrees*dtor) print "Cos: ";COS(radians);" "; COS(degrees*dtor) print "Tan: ";TAN(radians);" ";TAN(degrees*dtor) print "- Inverse functions:" print "Asn: ";ASN(SIN(radians));" Rad, "; ASN(SIN(degrees*dtor))*rtod;" Deg" print "Acs: ";ACS(COS(radians));" Rad, "; ACS(COS(degrees*dtor))*rtod;" Deg" print "Atn: ";ATN(TAN(radians));" Rad, "; ATN(TAN(degrees*dtor))*rtod;" Deg"</lang>

Output:

Sin:  0.70710678    0.70710678
Cos:  0.70710678    0.70710678
Tan:  1.0           1.0
-  Inverse functions:
Asn:   0.78539816 Rad,  45.0 Deg
Acs:   0.78539816 Rad,  45.0 Deg
Atn:   0.78539816 Rad,  45.0 Deg

Logo

UCB Logo has sine, cosine, and arctangent; each having variants for degrees or radians. <lang logo>print sin 45 print cos 45 print arctan 1 make "pi (radarctan 0 1) * 2 ; based on quadrant if uses two parameters print radsin :pi / 4 print radcos :pi / 4 print 4 * radarctan 1</lang>

Lhogho has pi defined in its trigonometric functions. Otherwise the same as UCB Logo. <lang logo>print sin 45 print cos 45 print arctan 1 print radsin pi / 4 print radcos pi / 4 print 4 * radarctan 1</lang>

Logtalk

- object(trignomeric_functions).

   :- public(show/0).
   show :-
       % standard trignomeric functions work with radians
       write('sin(pi/4.0) = '), SIN is sin(pi/4.0), write(SIN), nl,
       write('cos(pi/4.0) = '), COS is cos(pi/4.0), write(COS), nl,
       write('tan(pi/4.0) = '), TAN is tan(pi/4.0), write(TAN), nl,
       write('asin(sin(pi/4.0)) = '), ASIN is asin(sin(pi/4.0)), write(ASIN), nl,
       write('acos(cos(pi/4.0)) = '), ACOS is acos(cos(pi/4.0)), write(ACOS), nl,
       write('atan(tan(pi/4.0)) = '), ATAN is atan(tan(pi/4.0)), write(ATAN), nl,
       write('atan2(3,4) = '), ATAN2 is atan2(3,4), write(ATAN2), nl.

- end_object.

</lang>

Output:

<lang text> ?- trignomeric_functions::show. sin(pi/4.0) = 0.7071067811865475 cos(pi/4.0) = 0.7071067811865476 tan(pi/4.0) = 0.9999999999999999 asin(sin(pi/4.0)) = 0.7853981633974482 acos(cos(pi/4.0)) = 0.7853981633974483 atan(tan(pi/4.0)) = 0.7853981633974483 atan2(3,4) = 0.6435011087932844 yes </lang>

Lua

<lang lua>print(math.cos(1), math.sin(1), math.tan(1), math.atan(1), math.atan2(3, 4))</lang>

Maple

In radians: <lang Maple>sin(Pi/3); cos(Pi/3); tan(Pi/3);</lang>

Output:

> sin(Pi/3);
                                 1/2
                                3
                                ----
                                 2
> cos(Pi/3);
                                1/2

> tan(Pi/3);
                                 1/2
                                3

The equivalent in degrees with identical output: <lang Maple>with(Units[Standard]): sin(60*Unit(degree)); cos(60*Unit(degree)); tan(60*Unit(degree));</lang>

Note, Maple also has secant, cosecant, and cotangent: <lang Maple>csc(Pi/3); sec(Pi/3); cot(Pi/3);</lang>

Finally, the inverse trigonometric functions: <lang Maple>arcsin(1); arccos(1); arctan(1);</lang>

Output:

> arcsin(1);
                 Pi
                ----
                 2

> arccos(1);
                  0

> arctan(1);
                 Pi
                ----
                 4

Lastly, Maple also supports the two-argument arctan plus all the hyperbolic trigonometric functions.

Mathematica

<lang Mathematica>Sin[1] Cos[1] Tan[1] ArcSin[1] ArcCos[1] ArcTan[1] Sin[90 Degree] Cos[90 Degree] Tan[90 Degree] </lang>

MATLAB

A full list of built-in trig functions can be found in the MATLAB Documentation.

<lang MATLAB>function trigExample(angleDegrees)

   angleRadians = angleDegrees * (pi/180);
   
   disp(sprintf('sin(%f)= %f\nasin(%f)= %f',[angleRadians sin(angleRadians) sin(angleRadians) asin(sin(angleRadians))]));
   disp(sprintf('sind(%f)= %f\narcsind(%f)= %f',[angleDegrees sind(angleDegrees) sind(angleDegrees) asind(sind(angleDegrees))]));
   disp('-----------------------');
   disp(sprintf('cos(%f)= %f\nacos(%f)= %f',[angleRadians cos(angleRadians) cos(angleRadians) acos(cos(angleRadians))]));
   disp(sprintf('cosd(%f)= %f\narccosd(%f)= %f',[angleDegrees cosd(angleDegrees) cosd(angleDegrees) acosd(cosd(angleDegrees))]));
   disp('-----------------------');
   disp(sprintf('tan(%f)= %f\natan(%f)= %f',[angleRadians tan(angleRadians) tan(angleRadians) atan(tan(angleRadians))]));
   disp(sprintf('tand(%f)= %f\narctand(%f)= %f',[angleDegrees tand(angleDegrees) tand(angleDegrees) atand(tand(angleDegrees))]));

end</lang>

Output:

<lang MATLAB>>> trigExample(78) sin(1.361357)= 0.978148 asin(0.978148)= 1.361357 sind(78.000000)= 0.978148 arcsind(0.978148)= 78.000000

cos(1.361357)= 0.207912 acos(0.207912)= 1.361357 cosd(78.000000)= 0.207912 arccosd(0.207912)= 78.000000

tan(1.361357)= 4.704630 atan(4.704630)= 1.361357 tand(78.000000)= 4.704630 arctand(4.704630)= 78.000000</lang>

Maxima

<lang maxima>a: %pi / 3; [sin(a), cos(a), tan(a), sec(a), csc(a), cot(a)];

b: 1 / 2; [asin(b), acos(b), atan(b), asec(1 / b), acsc(1 / b), acot(b)];

/* Hyperbolic functions are also available */ a: 1 / 2; [sinh(a), cosh(a), tanh(a), sech(a), csch(a), coth(a)], numer; [asinh(a), acosh(1 / a), atanh(a), asech(a), acsch(a), acoth(1 / a)], numer;</lang>

MAXScript

Maxscript trigonometric functions accept degrees only. The built-ins degToRad and radToDeg allow easy conversion. <lang maxscript>local radians = pi / 4 local degrees = 45.0

--sine print (sin (radToDeg radians)) print (sin degrees) --cosine print (cos (radToDeg radians)) print (cos degrees) --tangent print (tan (radToDeg radians)) print (tan degrees) --arcsine print (asin (sin (radToDeg radians))) print (asin (sin degrees)) --arccosine print (acos (cos (radToDeg radians))) print (acos (cos degrees)) --arctangent print (atan (tan (radToDeg radians))) print (atan (tan degrees))</lang>

Metafont

Metafont has sind and cosd, which compute sine and cosine of an angle expressed in degree. We need to define the rest.

<lang metafont>Pi := 3.14159; vardef torad expr x = Pi*x/180 enddef; % conversions vardef todeg expr x = 180x/Pi enddef; vardef sin expr x = sind(todeg(x)) enddef; % radians version of sind vardef cos expr x = cosd(todeg(x)) enddef; % and cosd

vardef sign expr x = if x>=0: 1 else: -1 fi enddef; % commodity

vardef tand expr x = % tan with arg in degree

 if cosd(x) = 0:
   infinity * sign(sind(x))
 else: sind(x)/cosd(x) fi enddef;

vardef tan expr x = tand(todeg(x)) enddef; % arg in rad

% INVERSE

% the arc having x as tanget is that between x-axis and a line % from the center to the point (1, x); MF angle says this vardef atand expr x = angle(1,x) enddef; vardef atan expr x = torad(atand(x)) enddef; % rad version

% known formula to express asin and acos in function of % atan; a+-+b stays for sqrt(a^2 - b^2) (defined in plain MF) vardef asin expr x = 2atan(x/(1+(1+-+x))) enddef; vardef acos expr x = 2atan((1+-+x)/(1+x)) enddef;

vardef asind expr x = todeg(asin(x)) enddef; % degree versions vardef acosd expr x = todeg(acos(x)) enddef;

% commodity def outcompare(expr a, b) = message decimal a & " = " & decimal b enddef;

% output tests outcompare(torad(60), Pi/3); outcompare(todeg(Pi/6), 30);

outcompare(Pi/3, asin(sind(60))); outcompare(30, acosd(cos(Pi/6))); outcompare(45, atand(tand(45))); outcompare(Pi/4, atan(tand(45)));

outcompare(sin(Pi/3), sind(60)); outcompare(cos(Pi/4), cosd(45)); outcompare(tan(Pi/3), tand(60));

end</lang>

МК-61/52

sin	С/П	Вx	cos	С/П	Вx	tg	С/П	Вx	arcsin
С/П	Вx	arccos	С/П	Вx	arctg	С/П

Setting the units of angle (degrees, radians, grads) takes care of the switch Р-ГРД-Г.

NetRexx

<lang NetRexx>/* NetRexx */ options replace format comments java crossref symbols nobinary utf8

numeric digits 30

parse 'Radians Degrees angle' RADIANS DEGREES ANGLE .; parse 'sine cosine tangent arcsine arccosine arctangent' SINE COSINE TANGENT ARCSINE ARCCOSINE ARCTANGENT .

trigVals = trigVals[RADIANS, ANGLE ] = (Rexx Math.PI) / 4 -- Pi/4 == 45 degrees trigVals[DEGREES, ANGLE ] = 45.0 trigVals[RADIANS, SINE ] = (Rexx Math.sin(trigVals[RADIANS, ANGLE])) trigVals[DEGREES, SINE ] = (Rexx Math.sin(Math.toRadians(trigVals[DEGREES, ANGLE]))) trigVals[RADIANS, COSINE ] = (Rexx Math.cos(trigVals[RADIANS, ANGLE])) trigVals[DEGREES, COSINE ] = (Rexx Math.cos(Math.toRadians(trigVals[DEGREES, ANGLE]))) trigVals[RADIANS, TANGENT ] = (Rexx Math.tan(trigVals[RADIANS, ANGLE])) trigVals[DEGREES, TANGENT ] = (Rexx Math.tan(Math.toRadians(trigVals[DEGREES, ANGLE]))) trigVals[RADIANS, ARCSINE ] = (Rexx Math.asin(trigVals[RADIANS, SINE])) trigVals[DEGREES, ARCSINE ] = (Rexx Math.toDegrees(Math.acos(trigVals[DEGREES, SINE]))) trigVals[RADIANS, ARCCOSINE ] = (Rexx Math.acos(trigVals[RADIANS, COSINE])) trigVals[DEGREES, ARCCOSINE ] = (Rexx Math.toDegrees(Math.acos(trigVals[DEGREES, COSINE]))) trigVals[RADIANS, ARCTANGENT] = (Rexx Math.atan(trigVals[RADIANS, TANGENT])) trigVals[DEGREES, ARCTANGENT] = (Rexx Math.toDegrees(Math.atan(trigVals[DEGREES, TANGENT])))

return </lang>

Output:

            |           Radians |           Degrees |
       angle|    0.785398163397 |   45.000000000000 |
        sine|    0.707106781187 |    0.707106781187 |
      cosine|    0.707106781187 |    0.707106781187 |
     tangent|    1.000000000000 |    1.000000000000 |
     arcsine|    0.785398163397 |   45.000000000000 |
   arccosine|    0.785398163397 |   45.000000000000 |
  arctangent|    0.785398163397 |   45.000000000000 |

Nim

<lang nim>import math

proc radians(x): float = x * Pi / 180 proc degrees(x): float = x * 180 / Pi

let rad = Pi/4 let deg = 45.0

echo "Sine: ", sin(rad), " ", sin(radians(deg)) echo "Cosine : ", cos(rad), " ", cos(radians(deg)) echo "Tangent: ", tan(rad), " ", tan(radians(deg)) echo "Arcsine: ", arcsin(sin(rad)), " ", degrees(arcsin(sin(radians(deg)))) echo "Arccocose: ", arccos(cos(rad)), " ", degrees(arccos(cos(radians(deg)))) echo "Arctangent: ", arctan(tan(rad)), " ", degrees(arctan(tan(radians(deg))))</lang>

OCaml

OCaml's preloaded Pervasives module contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees. <lang ocaml>let pi = 4. *. atan 1.

let radians = pi /. 4. let degrees = 45.;;

Printf.printf "%f %f\n" (sin radians) (sin (degrees *. pi /. 180.));; Printf.printf "%f %f\n" (cos radians) (cos (degrees *. pi /. 180.));; Printf.printf "%f %f\n" (tan radians) (tan (degrees *. pi /. 180.));; let arcsin = asin (sin radians);; Printf.printf "%f %f\n" arcsin (arcsin *. 180. /. pi);; let arccos = acos (cos radians);; Printf.printf "%f %f\n" arccos (arccos *. 180. /. pi);; let arctan = atan (tan radians);; Printf.printf "%f %f\n" arctan (arctan *. 180. /. pi);;</lang>

Output:

0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45.000000
0.785398 45.000000
0.785398 45.000000

Octave

<lang octave>function d = degree(rad)

 d = 180*rad/pi;

endfunction

r = pi/3; rd = degree(r);

funcs = { "sin", "cos", "tan", "sec", "cot", "csc" }; ifuncs = { "asin", "acos", "atan", "asec", "acot", "acsc" };

for i = 1 : numel(funcs)

 v = arrayfun(funcs{i}, r);
 vd = arrayfun(strcat(funcs{i}, "d"), rd);
 iv = arrayfun(ifuncs{i}, v);
 ivd = arrayfun(strcat(ifuncs{i}, "d"), vd);
 printf("%s(%f) = %s(%f) = %f (%f)\n",
                   funcs{i}, r, strcat(funcs{i}, "d"), rd, v, vd);
 printf("%s(%f) = %f\n%s(%f) = %f\n",
                   ifuncs{i}, v, iv,
                   strcat(ifuncs{i}, "d"), vd, ivd);

endfor</lang>

Output:

sin(1.047198) = sind(60.000000) = 0.866025 (0.866025)
asin(0.866025) = 1.047198
asind(0.866025) = 60.000000
cos(1.047198) = cosd(60.000000) = 0.500000 (0.500000)
acos(0.500000) = 1.047198
acosd(0.500000) = 60.000000
tan(1.047198) = tand(60.000000) = 1.732051 (1.732051)
atan(1.732051) = 1.047198
atand(1.732051) = 60.000000
sec(1.047198) = secd(60.000000) = 2.000000 (2.000000)
asec(2.000000) = 1.047198
asecd(2.000000) = 60.000000
cot(1.047198) = cotd(60.000000) = 0.577350 (0.577350)
acot(0.577350) = 1.047198
acotd(0.577350) = 60.000000
csc(1.047198) = cscd(60.000000) = 1.154701 (1.154701)
acsc(1.154701) = 1.047198
acscd(1.154701) = 60.000000

(Lacking in this code but present in GNU Octave: sinh, cosh, tanh, coth and inverses)

Oforth

<lang Oforth>func: testTrigo { | rad deg hyp z |

  Pi 4 / ->rad 
  45.0   ->deg
   0.5   ->hyp

  System.Out rad sin << " - " << deg asRadian sin << cr 
  System.Out rad cos << " - " << deg asRadian cos << cr 
  System.Out rad tan << " - " << deg asRadian tan << cr

  printcr

  rad sin asin ->z   
  System.Out z << " - " << z asDegree << cr

  rad cos acos ->z   
  System.Out z << " - " << z asDegree << cr

  rad tan atan ->z   
  System.Out z << " - " << z asDegree << cr
  
  printcr

  System.Out hyp sinh << " - " << hyp sinh asinh << cr 
  System.Out hyp cosh << " - " << hyp cosh acosh << cr 
  System.Out hyp tanh << " - " << hyp tanh atanh << cr

}</lang>

Output:

0.707106781186547 - 0.707106781186547
0.707106781186548 - 0.707106781186548
1 - 1

0.785398163397448 - 45
0.785398163397448 - 45
0.785398163397448 - 45

0.521095305493747 - 0.5
1.12762596520638 - 0.5
0.46211715726001 - 0.5

ooRexx

rxm.cls                                                    20 March 2014

The distribution of ooRexx contains a function package called rxMath
that provides the computation of trigonometric and some other functions.
Based on the underlying C-library the precision of the returned values
is limited to 16 digits. Close observation show that sometimes the last
one to three digits of the returned values are not correct.
Many years ago I experimented with implementing these functions in Rexx
with its virtually unlimited precision.
The rxm class is intended to provide the same functionality as rxMath
with no limit on the specified or implied precision.

Functions in class rxm and invocation syntax are the same as
in the rxMath library. They are implemented as routines which
perform the checking of argument values and invoke the corresponding
methods. Here is a list of the supported functions and a concise
syntax specification.

The arguments are represented by these letters:

x is the value for which the respective function must be evaluated.
b and c for RxCalcPower are base and exponent, respectively.

p if specified is the desired precision (number of digits) in the result.
  It can be any integer from 1 to 999999.
  See below for the default used.

u if specified, is the unit of x given to the trigonometric functions
  or the unit of the value returned by the Arcus functions.
  It can be 'R', 'D', or 'G' for radians, degrees, or grades, respectively.
  See below for the default used.

Trigonometric functions:

• rxmCos(x[,[p][,u]])
• rxmCotan(x[,[p][,u]])
• rxmSin(x[,[p][,u]])
• rxmTan(x[,[p][,u]])

Arcus functions:

• rxmArcCos(x[,[p][,u]])
• rxmArcSin(x[,[p][,u]])
• rxmArcTan(x[,[p][,u]])

Hyperbolic functions:

• rxmCosH(x[,p])
• rxmSinH(x[,p])
• rxmTanH(x[,p])

• rxmExp(x[,p])      e**x
• rxmLog(x[,p])      Natural logarithm of x
• rxmLog10(x[,p])    Brigg's logarithm of x
• rxmSqrt(x[,p])     Square root of x

• rxmPower(b,c[,p])  b**c

• rxmPi([p])         pi to the specified or default precision

Values used for p and u if these are omitted in the invocation
==============================================================

The directive ::REQUIRES rxm.cls creates an instance of the class
  .local~my.rxm=.rxm~new(16,"D")
which sets the defaults for p=16 and u='D'.
These are used when p or u are omitted in a function invocation.
They can be changed by changing the respective class attributes as follows:
  .locaL~my.rxm~precision=50
  .locaL~my.rxm~type='R'
The current setting of these attributes can be retrieved as follows:
  .locaL~my.rxm~precision()
  .locaL~my.rxm~type()

While I tried to get full compatibility there remain a few
(actually very few) differences:

  rxCalcTan(90) raises the Syntax condition (will be fixed in the next ooRexx release)
  rxCalcexp(x) limits x to 709. or so and returns '+infinity' for larger exponents

<lang oorexx>/* REXX ---------------------------------------------------------------

show how the functions can be used
03.05.2014 Walter Pachl
--------------------------------------------------------------------*/

Say 'Default precision:' .locaL~my.rxm~precision() Say 'Default type: ' .locaL~my.rxm~type() Say 'rxmsin(60) ='rxmsin(60) -- use default precision and type Say 'rxmsin(1,21,"R")='rxmsin(1,21,'R') -- precision and type specified Say 'rxmlog(-1) ='rxmlog(-1) Say 'rxmlog( 0) ='rxmlog( 0) Say 'rxmlog( 1) ='rxmlog( 1) Say 'rxmlog( 2) ='rxmlog( 2)

 .locaL~my.rxm~precision=50
 .locaL~my.rxm~type='R'

Say 'Changed precision:' .locaL~my.rxm~precision() Say 'Changed type: ' .locaL~my.rxm~type() Say 'rxmsin(1) ='rxmsin(1) -- use changed precision and type

requires rxm.cls</lang>

Output:

Default precision: 16
Default type:      D
rxmsin(60)      =0.8660254037844386
rxmsin(1,21,"R")=0.841470984807896506653
rxmlog(-1)      =nan
rxmlog( 0)      =-infinity
rxmlog( 1)      =0
rxmlog( 2)      =0.6931471805599453
Changed precision: 50
Changed type:      R
rxmsin(1)       =0.84147098480789650665250232163029899962256306079837

<lang oorexx>/********************************************************************

Package rxm
implements the functions available in RxMath with high precision
by computing the values with significantly increased precision
and rounding the result to the specified precision.
This started 10 years ago when Vladimir Zabrodsky published his
Album of Algorithms http://dhost.info/zabrodskyvlada/aat/
Gerard Schildberger suggests on rosettacode.org to use +10 digits
Rony Flatscher suggested and helped to turn this into an ooRexx class
Rick McGuire advised on using Use STRICT Arg for argument checking
Alexander Seik creates this documentation
Horst Wegscheider helped with reviewing and some improvements
12.04.2014 Walter Pachl
Documentation: see rxmath.pdf in the ooRexx distribution
and rxm.doc (here)
13.04.2014 WP arcsin and arctan commentary corrected (courtesy Horst)
13.04.2014 WP improve arctan performance
20.04.2014 WP towards completion
24.04.2014 WP arcsin verbessert. courtesy Horst Wegscheider
28.04.2014 WP run ooRexxDoc
11.08.2014 WP replace log algorithm with Vladimir Zabrodsky's code
- - - - /

.local~my.rxm=.rxm~new(16,"D")

Class rxm Public

Method init

 Expose precision type
 Use Arg  precision=(digits()),type='D'

attribute precision set

 Expose precision
 Use Strict Arg  precision=(digits())

attribute precision get

attribute type set

 Expose type
 Use Strict Arg type='R'

attribute type get

Method arccos

/***********************************************************************

Return arccos(x,precision,type) -- with specified precision
arccos(x) = pi/2 - arcsin(x)
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10
 Numeric Digits iprec
 If x=1 Then
   r=0
 Else Do
   r=self~arcsin(x,iprec,'R')
   If r='nan' Then
     Return r
   r=self~pi(iprec)/2 - r
   End
 Select
   When xtype='D' Then
     r=r*180/self~pi(iprec)
   When xtype='G' Then
     r=r*200/self~pi(iprec)
   Otherwise
     Nop
   End
 Numeric Digits xprec
 Return (r+0)

Method arcsin

/***********************************************************************

Return arcsin(x,precision,type) -- with specified precision
arcsin(x) = x+(x**3)*1/2*3+(x**5)*1*3/2*4*5+(x**7)*1*3*5/2*4*6*7+...
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10
 Numeric Digits iprec
 sign=sign(x)
 If x<0 Then
   x=abs(x)
 Select
   When abs(x)>1 Then
     Return 'nan'
   When x=0 Then
     r=0
   When x=1 Then
     r=rxmpi(iprec)/2
   When x<0.8 Then Do
     o=x
     u=1
     r=x
     Do i=3 By 2 Until ra=r
       ra=r
       o=o*x*x*(i-2)
       u=u*(i-1)*i/(i-2)
       r=r+(o/u)
       If r=ra Then
         r=r+(o/u)/2 /* final touch */
       End
     End
   Otherwise Do
     z=x
     r=x
     o=x
     s=x*x
     do j=2 by 2;
       o=o*s*(j-1)/j;
       z=z+o/(j+1);
       if z=r then
         leave
       r=z;
       end
     /***********************
     y=(1-x*x)/4
     n=0.5-self~sqrt(y,iprec)
     z=self~sqrt(n,iprec)
     r=2*self~arcsin(z,xprec)
     ***********************/
     End
   End
 Select
   When xtype='D' Then
     r=r*180/self~pi(iprec)
   When xtype='G' Then
     r=r*200/self~pi(iprec)
   Otherwise
     Nop
   End
 Numeric Digits xprec
 Return sign*(r+0)

Method arctan

/***********************************************************************

Return arctan(x,precision,type) -- with specified precision
x=0 -> arctan(x) = 0
If x>0 Then
x<1 -> arctan(x) = arcsin(x/sqrt(x**2+1))
x=1 -> arctan(x) = pi/4
x>1 -> arctan(x) = pi/2-arcsin((1/x)/sqrt((1/x)**2+1))
Else
adjust as necessary
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10
 Numeric Digits iprec
 Select
   When abs(x)<1 Then
     r=self~arcsin(x/self~sqrt(1+x**2,iprec),iprec,'R')
   When abs(x)=1 Then
     r=self~pi(iprec)/4*sign(x)
   Otherwise Do
     xr=1/abs(x)
     r=self~arcsin(xr/self~sqrt(1+xr**2,iprec),iprec,'R')
     If x>0 Then
       r=self~pi(iprec)/2-r
     Else
       r=-self~pi(iprec)/2+r
     End
   End
 Select
   When xtype='D' Then
     r=r*180/self~pi(iprec)
   When xtype='G' Then
     r=r*200/self~pi(iprec)
   Otherwise
     Nop
   End
 Numeric Digits xprec
 Return (r+0)

Method arsinh

/***********************************************************************

Return arsinh(x,precision,type) -- with specified precision
arsinh(x) = ln(x+sqrt(x**2+1))
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision)
 iprec=xprec+10
 Numeric Digits iprec
 x2p1=x**2+1
 r=self~log(x+self~sqrt(x2p1,iprec),iprec)
 Numeric Digits xprec
 Return (r+0)

Method cos

/* REXX *************************************************************

Return cos(x,precision,type) -- with the specified precision
cos(x)=sin(x+pi/2)
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10
 Numeric Digits iprec
 Select
   When xtype='R' Then xa=x+self~pi(iprec)/2
   When xtype='D' Then xa=x+90
   When xtype='G' Then xa=x+100
   End
 r=self~sin(xa,iprec,xtype)
 Numeric Digits xprec
 Return (r+0)

Method cosh

/* REXX ****************************************************************

Return cosh(x,precision,type) -- with specified precision
cosh(x) = 1+(x**2/2!)+(x**4/4!)+(x**6/6!)+-...
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision)
 iprec=xprec+10
 Numeric Digits iprec
 o=1
 u=1
 r=1
 Do i=2 By 2 Until ra=r
   ra=r
   o=o*x*x
   u=u*i*(i-1)
   r=r+(o/u)
   End
 Numeric Digits xprec
 Return (r+0)

Method cotan

/* REXX *************************************************************

Return cotan(x,precision,type) -- with the specified precision
cot(x)=cos(x)/sin(x)
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10
 Numeric Digits iprec
 s=self~sin(x,iprec,xtype)
 c=self~cos(x,iprec,xtype)
 If s=0 Then
   Return '+infinity'
 r=c/s
 Numeric Digits xprec
 Return (r+0)

Method exp

/***********************************************************************

exp(x,precision) returns e**x -- with specified precision
exp(x,precision,base) returns base**x -- with specified precision
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision),xbase=
 iprec=xprec+10
 Numeric Digits iprec
 Numeric Fuzz   3
 If xbase<> Then Do
   Select
     When xbase=0 Then Do
       Select
         When x<0 Then Return '+infinity'
         When x=0 Then Return 'nan'
         Otherwise Return 0
         End
       End
     When xbase=1 Then Return 1
     When xbase<0 Then Do
       Select
         When x=0 Then Return 1
         When datatype(x,'W')=0 Then Return 'nan'
         Otherwise Do
           r=xbase**x
           Numeric Digits xprec
           Return r+0
           End
         End
       End
     Otherwise
       x=x*self~log(xbase,iprec)
     End
   End
 o=1
 u=1
 r=1
 Do i=1 By 1 Until ra=r
   ra=r
   o=o*x
   u=u*i
   r=r+(o/u)
   End
 Numeric Digits xprec
 Return (r+0)

Method log

/***********************************************************************

log(x,precision) -- returns ln(x) with specified precision
log(x,precision,base) -- returns blog(x) with specified precision
Three different series are used for ln(x): x in range 0 to 0.5
0.5 to 1.5
1.5 to infinity
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision),xbase=
 iprec=xprec+100
 Numeric Digits iprec
 Select
   When x=0 Then Return '-infinity'
   When x<0 Then Return 'nan'
   When x<1 Then  r= -self~Log(1/X,xprec)
   Otherwise Do
     do M = 0 until (2 ** M) > X; end
     M = M - 1
     Z = X / (2 ** M)
     Zeta = (1 - Z) / (1 + Z)
     N = Zeta; Ln = Zeta; Zetasup2 = Zeta * Zeta
     do J = 1
       N = N * Zetasup2; NewLn = Ln + N / (2 * J + 1)
       if NewLn = Ln then Do
         r= M * self~LN2P(xprec) - 2 * Ln
         Leave
         End
       Ln = NewLn
       end
     End
   End
 If x>0 Then Do
   If xbase> Then
     r=r/self~log(xbase,iprec)
 Numeric Digits xprec
   r=r+0
   End
 Return r

Method ln2p

 Parse Arg p
 Numeric Digits p+10
 If p<=1000 Then
   Return self~ln2()
 n=1/3
 ln=n
 zetasup2=1/9
 Do j=1
   n=n*zetasup2
   newln=ln+n/(2*j+1)
   If newln=ln Then
     Return 2*ln
   ln=newln
   End

Method LN2

   V = 
   V = V || 0.69314718055994530941723212145817656807
   V = V || 5500134360255254120680009493393621969694
   V = V || 7156058633269964186875420014810205706857
   V = V || 3368552023575813055703267075163507596193
   V = V || 0727570828371435190307038623891673471123350

v= v=v||0.69314718055994530941723212145817656807 v=v||5500134360255254120680009493393621969694 v=v||7156058633269964186875420014810205706857 v=v||3368552023575813055703267075163507596193 v=v||0727570828371435190307038623891673471123 v=v||3501153644979552391204751726815749320651 v=v||5552473413952588295045300709532636664265 v=v||4104239157814952043740430385500801944170 v=v||6416715186447128399681717845469570262716 v=v||3106454615025720740248163777338963855069 v=v||5260668341137273873722928956493547025762 v=v||6520988596932019650585547647033067936544 v=v||3254763274495125040606943814710468994650 v=v||6220167720424524529612687946546193165174 v=v||6813926725041038025462596568691441928716 v=v||0829380317271436778265487756648508567407 v=v||7648451464439940461422603193096735402574 v=v||4460703080960850474866385231381816767514 v=v||3866747664789088143714198549423151997354 v=v||8803751658612753529166100071053558249879 v=v||4147295092931138971559982056543928717000 v=v||7218085761025236889213244971389320378439 v=v||3530887748259701715591070882368362758984 v=v||2589185353024363421436706118923678919237 v=v||231467232172053401649256872747782344535348

   return V

Method log10

/***********************************************************************

Return log10(x,prec) specified precision
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision)
 iprec=xprec+10
 r=self~log(x,iprec,10)
 Numeric Digits xprec
 Return (r+0)

Method pi

/* REXX *************************************************************

Return pi with the specified precision
- - - - /

 Expose precision
 Use Strict Arg xprec=(precision)
 p='3.141592653589793238462643383279502884197169399375'||,
   '10582097494459230781640628620899862803482534211706'||,
   '79821480865132823066470938446095505822317253594081'||,
   '28481117450284102701938521105559644622948954930381'||,
   '96442881097566593344612847564823378678316527120190'||,
   '91456485669234603486104543266482133936072602491412'||,
   '73724587006606315588174881520920962829254091715364'||,
   '36789259036001133053054882046652138414695194151160'||,
   '94330572703657595919530921861173819326117931051185'||,
   '48074462379962749567351885752724891227938183011949'||,
   '12983367336244065664308602139494639522473719070217'||,
   '98609437027705392171762931767523846748184676694051'||,
   '32000568127145263560827785771342757789609173637178'||,
   '72146844090122495343014654958537105079227968925892'||,
   '35420199561121290219608640344181598136297747713099'||,
   '60518707211349999998372978049951059731732816096318'||,
   '59502445945534690830264252230825334468503526193118'||,
   '81710100031378387528865875332083814206171776691473'||,
   '03598253490428755468731159562863882353787593751957'||,
   '781857780532171226806613001927876611195909216420199'
 If xprec>1000 Then Do              /* more than 1000 digits wanted */
   iprec=xprec+10                     /* internal precision         */
   Numeric Digits iprec
   new=1
   a=sqrt(2,iprec)
   b=0
   p=2+a
   Do i=1 By 1 Until p=pi
     pi=p
     y=self~sqrt(a,iprec)
     a1=(y+1/y)/2
     b1=y*(b+1)/(b+a)
     p=pi*b1*(1+a1)/(1+b1)
     a=a1
     b=b1
     End
   End
 Numeric Digits xprec
 Return (p+0)

Method power

/***********************************************************************

power(base,exponent,precision) returns base**exponent
-- with specified precision
- - - - /

 Expose precision
 Use Strict Arg b,c,xprec=(precision)
 Numeric Digits xprec
 rsign=1
 If b<0 Then Do                       /* negative base              */
   If datatype(c,'W') Then Do         /* Exponent is an integer     */
     If c//2=1 Then                   /* .. an odd number           */
       rsign=-1                       /* Resuld will be negative    */
     b=abs(b)                         /* proceed with positive base */
     End
   Else Do                            /* Exponent is not an integer */

-- Say 'for a negative base ('||b')',

                          'exponent ('c') must be an integer'
     Return 'nan'                     /* Return not a number        */
     End
   End
 If c=0 Then Do
   If b>=0 Then
     r=1
   End
 Else
   r=self~exp(c,xprec,b)
 If datatype(r)<>'NUM' Then
   Return r
 Return rsign*r

Method sqrt

/* REXX *************************************************************

Return sqrt(x,precision) -- with the specified precision
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision)
 If x<0 Then Do
   Return 'nan'
   End
 iprec=xprec+10
 Numeric Digits iprec
 r0= x
 r = 1
 Do i=1 By 1 Until r=r0 | (abs(r*r-x)<10**-iprec)
   r0 = r
   r  = (r + x/r) / 2
   End
 Numeric Digits xprec
 Return (r+0)

Method sin

/* REXX *************************************************************

Return sin(x,precision,type) -- with the specified precision
xtype = 'R' (radians, default) 'D' (degrees) 'G' (grades)
sin(x) = x-(x**3/3!)+(x**5/5!)-(x**7/7!)+-...
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10                       /* internal precision         */
 Numeric Digits iprec
 /* first use pi constant or compute it if necessary                */
 pi=self~pi(iprec)
 /* normalize x to be between 0 and 2*pi (or equivalent)            */
 /* and convert degrees or grades to radians                        */
 xx=x
 Select
   When xtype='R' Then Do
     Do While xx>=pi*2; xx=xx-pi*2; End
     Do While xx<0;     xx=xx+pi*2; End
     End
   When xtype='D' Then Do
     Do While xx>=360;  xx=xx-360; End
     Do While xx<0;     xx=xx+360; End
     xx=xx*pi/180
     End
   When xtype='G' Then Do
     Do While xx>=400;  xx=xx-400; End
     Do While xx<0;     xx=xx+400; End
     xx=xx*pi/200
     End
   End
 /* normalize xx to be between 0 and pi/2                            */
 sign=1
 Select
   When xx<=pi/2   Then Nop
   When xx<=pi     Then xx=pi-xx
   When xx<=3*pi/2 Then Do; sign=-1; xx=xx-pi; End
   Otherwise            Do; sign=-1; xx=2*pi-xx; End
   End
 /* now compute the Taylor series for the normalized xx             */
 o=xx
 u=1
 r=xx
 If abs(xx)<10**(-iprec) Then
   r=0
 Else Do
   Do i=3 By 2 Until ra=r
     ra=r
     o=-o*xx*xx
     u=u*i*(i-1)
     r=r+(o/u)
     End
   End
 Numeric Digits xprec
 Return sign*(r+0)

Method sinh

/* REXX ****************************************************************

Return sinh(x,precision) -- with specified precision
sinh(x) = x+(x**3/3!)+(x**5/5!)+(x**7/7!)+-...
920903 Walter Pachl
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision)
 iprec=xprec+10
 Numeric Digits iprec
 o=x
 u=1
 r=x
 Do i=3 By 2 Until ra=r
   ra=r
   o=o*x*x
   u=u*i*(i-1)
   r=r+(o/u)
   End
 Numeric Digits xprec
 Return (r+0)

Method tan

/* REXX *************************************************************

Return tan(x,precision,type) -- with the specified precision
tan(x)=sin(x)/cos(x)
- - - - /

 Expose precision type
 Use Strict Arg x,xprec=(precision),xtype=(type)
 iprec=xprec+10
 Numeric Digits iprec
 s=self~sin(x,iprec,xtype)
 c=self~cos(x,iprec,xtype)
 If c=0 Then
   Return '+infinity'
 t=s/c
 Numeric Digits xprec
 Return (t+0)

Method tanh

/***********************************************************************

Return tanh(x,precision) -- with specified precision
tanh(x) = sinh(x)/cosh(x)
- - - - /

 Expose precision
 Use Strict Arg x,xprec=(precision)
 iprec=xprec+10
 Numeric Digits iprec
 r=self~sinh(x,iprec)/self~cosh(x,iprec)
 Numeric Digits xprec
 Return (r+0)

routine rxmarccos public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If x<-1 | 1<x Then
   Return 'nan'

 return .my.rxm~arccos(x,xprec,xtype)

routine rxmarcsin public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If wordpos(xtype,'R D G')=0 Then Do

-- Say 'Argument 3 must be R, D, or G'

   Raise Syntax 88.907 array(3,'R, D, or G',xtype)
   End

 If x<-1 | 1<x Then
   Return 'nan'

 return .my.rxm~arcsin(x,xprec,xtype)

routine rxmarctan public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If wordpos(xtype,'R D G')=0 Then Do

-- Say 'Argument 3 must be R, D, or G'

   Raise Syntax 88.907 array(3,'R, D, or G',xtype)
   End

 return .my.rxm~arctan(x,xprec,xtype)

routine rxmarsinh public

 Use Strict Arg x,xprec=(.my.rxm~precision)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 return .my.rxm~arsinh(x,xprec)

routine rxmcos public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If wordpos(xtype,'R D G')=0 Then Do

-- Say 'Argument 3 must be R, D, or G'

   Raise Syntax 88.907 array(3,'R, D, or G',xtype)
   End

 return .my.rxm~cos(x,xprec,xtype)

routine rxmcosh public

 Use Strict Arg x,xprec=(.my.rxm~precision)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 return .my.rxm~cosh(x,xprec)

routine rxmcotan public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If wordpos(xtype,'R D G')=0 Then Do

-- Say 'Argument 3 must be R, D, or G'

   Raise Syntax 88.907 array(3,'R, D, or G',xtype)
   End

 return .my.rxm~cotan(x,xprec)

routine rxmexp public

 Use Strict Arg x,xprec=(.my.rxm~precision),xbase=
 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If datatype(xbase,'NUM')=0 & xbase<> Then Do

-- Say 'Argument 3 must be omitted or a number'

   Raise Syntax 88.902 array(3,xbase)
   End

 Select
   When x<0 Then Do
     iprec=xprec+10
     Numeric Digits iprec
     z=.my.rxm~exp(abs(x),iprec,xbase)
     Select
       When z=0 Then Return '+infinity'
       When datatype(z)<>'NUM' Then Return z
       Otherwise r=1/z
       End
     Numeric Digits xprec
     return r+0
     End
   When x=0 Then Do
     If xbase=0 Then
       Return 'nan'
     Else
       Return 1
     End
   Otherwise
     return .my.rxm~exp(x,xprec,xbase)
   End

routine rxmlog public

 Use Strict Arg x,xprec=(.my.rxm~precision),xbase=

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If xbase<> &,
    datatype(xbase,'NUM')=0 Then Do

-- Say 'Argument 3 must be a number'

   Raise Syntax 88.902 array(3,xbase)
   End

 If x=0 Then
   Return '-infinity'

 If x<0 Then
   Return 'nan'

 return .my.rxm~log(x,xprec,xbase)

routine rxmlog10 public

 Use Strict Arg x,xprec=(.my.rxm~precision)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If x=0 Then
   Return '-infinity'

 If x<0 Then
   Return 'nan'

 return .my.rxm~log10(x,xprec)

routine rxmpi public

 Use Strict Arg xprec=(.my.rxm~precision)

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 return .my.rxm~pi(xprec)

routine rxmpower public

 Use Strict Arg b,e,xprec=(.my.rxm~precision)

 If datatype(b,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,b)
   End

 If datatype(e,'NUM')=0 Then Do

-- Say 'Argument 2 must be a number'

   Raise Syntax 88.902 array(2,e)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 3 must be a whole number between 1 and 999999'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 3 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(3,1,999999,xprec)
   End

 If b<0 & datatype(e,'W')=0 Then
   Return 'nan'

 return .my.rxm~power(b,e,xprec)

routine rxmsqrt public

 Use Strict Arg x,xprec=(.my.rxm~precision)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End
 Select
   When x<0 Then Return 'nan'
   When x=0 Then Return 0
   Otherwise
     return .my.rxm~sqrt(x,xprec)
   End

routine rxmsin public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If wordpos(xtype,'R D G')=0 Then Do

-- Say 'Argument 3 must be R, D, or G'

   Raise Syntax 88.907 array(3,'R, D, or G',xtype)
   End

 return .my.rxm~sin(x,xprec,xtype)

routine rxmsinh public

 Use Strict Arg x,xprec=(.my.rxm~precision)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 return .my.rxm~sinh(x,xprec)

routine rxmtan public

 Use Strict Arg x,xprec=(.my.rxm~precision),xtype=(.my.rxm~type)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 If wordpos(xtype,'R D G')=0 Then Do

-- Say 'Argument 3 must be R, D, or G'

   Raise Syntax 88.907 array(3,'R, D, or G',xtype)
   End

 return .my.rxm~tan(x,xprec,xtype)

routine rxmtanh public

 Use Strict Arg x,xprec=(.my.rxm~precision)

 If datatype(x,'NUM')=0 Then Do

-- Say 'Argument 1 must be a number'

   Raise Syntax 88.902 array(1,x)
   End

 If datatype(xprec,'W')=0 Then Do

-- Say 'Argument 2 must be a positive whole number'

   Raise Syntax 88.905 array(2,xprec)
   End

 If xprec<1 | 999999<xprec Then Do

-- Say 'Argument 2 must be a whole number between 1 and 999999'

   Raise Syntax 88.907 array(2,1,999999,xprec)
   End

 return .my.rxm~tanh(x,xprec)

routine rxmhelp public

 Use Arg xprec=(.my.rxm~precision),xtype=(.my.rxm~type)
                  Say 'precision='xprec
                  Say '     type='xtype
 Parse source  s; Say '   source='s
 Parse version v; Say '  version='v
 Do si=2 To 5
   Say substr(sourceline(si),3)
   End
 Say 'You can change the default precision and type as follows:'
 Say "  .locaL~my.rxm~precision=50"
 Say "  .locaL~my.rxm~type='R'"
 return 0</lang>

Oz

<lang oz>declare

 PI = 3.14159265

 fun {FromDegrees Deg}
    Deg * PI / 180.
 end

 fun {ToDegrees Rad}
    Rad * 180. / PI
 end

 Radians = PI / 4.
 Degrees = 45.

in

 for F in [Sin Cos Tan] do
    {System.showInfo {F Radians}#"  "#{F {FromDegrees Degrees}}}
 end

 for I#F in [Asin#Sin Acos#Cos Atan#Tan] do
    {System.showInfo {I {F Radians}}#"  "#{ToDegrees {I {F Radians}}}}
 end</lang>

PARI/GP

Pari accepts only radians; the conversion is simple but not included here. <lang parigp>cos(Pi/2) sin(Pi/2) tan(Pi/2) acos(1) asin(1) atan(1)</lang>

Works with: PARI/GP version 2.4.3 and above

<lang parigp>apply(f->f(1), [cos,sin,tan,acos,asin,atan])</lang>

Pascal

Library: math

<lang pascal>Program TrigonometricFuntions(output);

uses

 math;

var

 radians, degree: double;

begin

 radians := pi / 4.0;
 degree := 45;
 //  Pascal works in radians.  Necessary degree-radian conversions are shown.
 writeln (sin(radians),'   ', sin(degree/180*pi));
 writeln (cos(radians),'   ', cos(degree/180*pi));
 writeln (tan(radians),'   ', tan(degree/180*pi));
 writeln ();
 writeln (arcsin(sin(radians)),' Rad., or ', arcsin(sin(degree/180*pi))/pi*180,' Deg.');
 writeln (arccos(cos(radians)),' Rad., or ', arccos(cos(degree/180*pi))/pi*180,' Deg.');
 writeln (arctan(tan(radians)),' Rad., or ', arctan(tan(degree/180*pi))/pi*180,' Deg.');
 //  ( radians ) / pi * 180 = deg.

end.</lang>

Output:

 7.0710678118654750E-0001    7.0710678118654752E-0001
 7.0710678118654755E-0001    7.0710678118654752E-0001
 9.9999999999999994E-0001    1.0000000000000000E+0000

 7.8539816339744828E-0001  Rad., or  4.5000000000000000E+0001  Deg.
 7.8539816339744828E-0001  Rad., or  4.5000000000000000E+0001  Deg.
 7.8539816339744828E-0001  Rad., or  4.5000000000000000E+0001  Deg.

Perl

Works with: Perl version 5.8.8

<lang perl>use Math::Trig;

my $angle_degrees = 45; my $angle_radians = pi / 4;

print sin($angle_radians), ' ', sin(deg2rad($angle_degrees)), "\n"; print cos($angle_radians), ' ', cos(deg2rad($angle_degrees)), "\n"; print tan($angle_radians), ' ', tan(deg2rad($angle_degrees)), "\n"; print cot($angle_radians), ' ', cot(deg2rad($angle_degrees)), "\n"; my $asin = asin(sin($angle_radians)); print $asin, ' ', rad2deg($asin), "\n"; my $acos = acos(cos($angle_radians)); print $acos, ' ', rad2deg($acos), "\n"; my $atan = atan(tan($angle_radians)); print $atan, ' ', rad2deg($atan), "\n"; my $acot = acot(cot($angle_radians)); print $acot, ' ', rad2deg($acot), "\n";</lang>

Output:

0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
1 1
1 1
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45

Perl 6

Works with: Rakudo version #22 "Thousand Oaks"

<lang perl6>say sin(pi/3), ' ', sin 60, 'd'; # 'g' (gradians) and 1 (circles) say cos(pi/4), ' ', cos 45, 'd'; # are also recognized. say tan(pi/6), ' ', tan 30, 'd';

say asin(sqrt(3)/2), ' ', asin sqrt(3)/2, 'd'; say acos(1/sqrt 2), ' ', acos 1/sqrt(2), 'd'; say atan(1/sqrt 3), ' ', atan 1/sqrt(3), 'd';</lang>

PL/I

<lang PL/I> declare (x, xd, y, v) float;

x = 0.5; xd = 45;

/* angle in radians: */ v = sin(x); y = asin(v); put skip list (y); v = cos(x); y = acos(v); put skip list (y); v = tan(x); y = atan(v); put skip list (y);

/* angle in degrees: */ v = sind(xd); put skip list (v); v = cosd(xd); put skip list (v); v = tand(xd); y = atand(v); put skip list (y);

/* hyperbolic functions: */ v = sinh(x); put skip list (v); v = cosh(x); put skip list (v); v = tanh(x); y = atanh(v); put skip list (y); </lang> Results:

 5.00000E-0001 
 5.00000E-0001 
 5.00000E-0001 
 7.07107E-0001 
 7.07107E-0001 
 4.50000E+0001 
 5.21095E-0001 
 1.12763E+0000 
 5.00000E-0001

PL/SQL

The transcendental functions COS, COSH, EXP, LN, LOG, SIN, SINH, SQRT, TAN, and TANH are accurate to 36 decimal digits. The transcendental functions ACOS, ASIN, ATAN, and ATAN2 are accurate to 30 decimal digits.

<lang plsql>DECLARE

 pi NUMBER := 4 * atan(1);
 radians NUMBER := pi / 4;
 degrees NUMBER := 45.0;

BEGIN

 DBMS_OUTPUT.put_line(SIN(radians) || ' ' || SIN(degrees * pi/180) );
 DBMS_OUTPUT.put_line(COS(radians) || ' ' || COS(degrees * pi/180) );
 DBMS_OUTPUT.put_line(TAN(radians) || ' ' || TAN(degrees * pi/180) );
 DBMS_OUTPUT.put_line(ASIN(SIN(radians)) || ' ' || ASIN(SIN(degrees * pi/180)) * 180/pi);
 DBMS_OUTPUT.put_line(ACOS(COS(radians)) || ' ' || ACOS(COS(degrees * pi/180)) * 180/pi);
 DBMS_OUTPUT.put_line(ATAN(TAN(radians)) || ' ' || ATAN(TAN(degrees * pi/180)) * 180/pi);

end;</lang>

Output:

,7071067811865475244008443621048490392889 ,7071067811865475244008443621048490392893
,7071067811865475244008443621048490392783 ,7071067811865475244008443621048490392779
1,00000000000000000000000000000000000001 1,00000000000000000000000000000000000002
,7853981633974483096156608458198656891236 44,99999999999999999999999999999942521259
,7853981633974483096156608458198857529988 45,00000000000000000000000000000057478811
,7853981633974483096156608458198757210578 45,00000000000000000000000000000000000067

The following trigonometric functions are also available <lang plsql>ATAN2(n1,n2) --Arctangent(y/x), -pi < result <= +pi SINH(n) --Hyperbolic sine COSH(n) --Hyperbolic cosine TANH(n) --Hyperbolic tangent</lang>

PHP

<lang php>$radians = M_PI / 4; $degrees = 45 * M_PI / 180; echo sin($radians) . " " . sin($degrees); echo cos($radians) . " " . cos($degrees); echo tan($radians) . " " . tan($degrees); echo asin(sin($radians)) . " " . asin(sin($radians)) * 180 / M_PI; echo acos(cos($radians)) . " " . acos(cos($radians)) * 180 / M_PI; echo atan(tan($radians)) . " " . atan(tan($radians)) * 180 / M_PI;</lang>

PicoLisp

<lang PicoLisp>(load "@lib/math.l")

(de dtor (Deg)

  (*/ Deg pi 180.0) )

(de rtod (Rad)

  (*/ Rad 180.0 pi) )

(prinl

  (format (sin (/ pi 4)) *Scl) " " (format (sin (dtor 45.0)) *Scl) )

(prinl

  (format (cos (/ pi 4)) *Scl) " " (format (cos (dtor 45.0)) *Scl) )

(prinl

  (format (tan (/ pi 4)) *Scl) " " (format (tan (dtor 45.0)) *Scl) )

(prinl

  (format (asin (sin (/ pi 4))) *Scl) " " (format (rtod (asin (sin (dtor 45.0)))) *Scl) )

(prinl

  (format (acos (cos (/ pi 4))) *Scl) " " (format (rtod (acos (cos (dtor 45.0)))) *Scl) )

(prinl

  (format (atan (tan (/ pi 4))) *Scl) " " (format (rtod (atan (tan (dtor 45.0)))) *Scl) )</lang>

Output:

0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 44.999986
0.785398 44.999986
0.785398 44.999986

Pop11

Pop11 trigonometric functions accept both degrees and radians. In default mode argument is in degrees, after setting 'popradians' flag to 'true' arguments are in radians.

<lang pop11>sin(30) => cos(45) => tan(45) => arcsin(0.7) => arccos(0.7) => arctan(0.7) =>

switch to radians

true -> popradians;

sin(pi*30/180) => cos(pi*45/180) => tan(pi*45/180) => arcsin(0.7) => arccos(0.7) => arctan(0.7) =></lang>

PostScript

<lang postscript> 90 sin =

60 cos =

%tan of 45 degrees

45 sin 45 cos div =

%inverse tan ( arc tan of sqrt 3)

3 sqrt 1 atan = </lang>

Output:

1.0

0.5

1.0

60.0

PowerShell

Translation of: C

<lang powershell>$rad = [Math]::PI / 4 $deg = 45 '{0,10} {1,10}' -f 'Radians','Degrees' '{0,10:N6} {1,10:N6}' -f [Math]::Sin($rad), [Math]::Sin($deg * [Math]::PI / 180) '{0,10:N6} {1,10:N6}' -f [Math]::Cos($rad), [Math]::Cos($deg * [Math]::PI / 180) '{0,10:N6} {1,10:N6}' -f [Math]::Tan($rad), [Math]::Tan($deg * [Math]::PI / 180) $temp = [Math]::Asin([Math]::Sin($rad)) '{0,10:N6} {1,10:N6}' -f $temp, ($temp * 180 / [Math]::PI) $temp = [Math]::Acos([Math]::Cos($rad)) '{0,10:N6} {1,10:N6}' -f $temp, ($temp * 180 / [Math]::PI) $temp = [Math]::Atan([Math]::Tan($rad)) '{0,10:N6} {1,10:N6}' -f $temp, ($temp * 180 / [Math]::PI)</lang>

Output:

   Radians    Degrees
  0,707107   0,707107
  0,707107   0,707107
  1,000000   1,000000
  0,785398  45,000000
  0,785398  45,000000
  0,785398  45,000000

PureBasic

<lang purebasic>OpenConsole()

Macro DegToRad(deg)

 deg*#PI/180

EndMacro Macro RadToDeg(rad)

 rad*180/#PI

EndMacro

degree = 45 radians.f = #PI/4

PrintN(StrF(Sin(DegToRad(degree)))+" "+StrF(Sin(radians))) PrintN(StrF(Cos(DegToRad(degree)))+" "+StrF(Cos(radians))) PrintN(StrF(Tan(DegToRad(degree)))+" "+StrF(Tan(radians)))

arcsin.f = ASin(Sin(radians)) PrintN(StrF(arcsin)+" "+Str(RadToDeg(arcsin))) arccos.f = ACos(Cos(radians)) PrintN(StrF(arccos)+" "+Str(RadToDeg(arccos))) arctan.f = ATan(Tan(radians)) PrintN(StrF(arctan)+" "+Str(RadToDeg(arctan)))

Input()</lang>

Output:

0.707107 0.707107
0.707107 0.707107
1.000000 1.000000
0.785398 45
0.785398 45
0.785398 45

Python

Python's math module contains all six functions.
The functions all accept radians only, so conversion is necessary when dealing with degrees.
The math module also has degrees() and radians() functions for easy conversion.

<lang python>Python 3.2.2 (default, Sep 4 2011, 09:51:08) [MSC v.1500 32 bit (Intel)] on win32 Type "copyright", "credits" or "license()" for more information. >>> from math import degrees, radians, sin, cos, tan, asin, acos, atan, pi >>> rad, deg = pi/4, 45.0 >>> print("Sine:", sin(rad), sin(radians(deg))) Sine: 0.7071067811865475 0.7071067811865475 >>> print("Cosine:", cos(rad), cos(radians(deg))) Cosine: 0.7071067811865476 0.7071067811865476 >>> print("Tangent:", tan(rad), tan(radians(deg))) Tangent: 0.9999999999999999 0.9999999999999999 >>> arcsine = asin(sin(rad)) >>> print("Arcsine:", arcsine, degrees(arcsine)) Arcsine: 0.7853981633974482 44.99999999999999 >>> arccosine = acos(cos(rad)) >>> print("Arccosine:", arccosine, degrees(arccosine)) Arccosine: 0.7853981633974483 45.0 >>> arctangent = atan(tan(rad)) >>> print("Arctangent:", arctangent, degrees(arctangent)) Arctangent: 0.7853981633974483 45.0 >>> </lang>

R

<lang R>deg <- function(radians) 180*radians/pi rad <- function(degrees) degrees*pi/180 sind <- function(ang) sin(rad(ang)) cosd <- function(ang) cos(rad(ang)) tand <- function(ang) tan(rad(ang)) asind <- function(v) deg(asin(v)) acosd <- function(v) deg(acos(v)) atand <- function(v) deg(atan(v))

r <- pi/3 rd <- deg(r)

print( c( sin(r), sind(rd)) ) print( c( cos(r), cosd(rd)) ) print( c( tan(r), tand(rd)) )

S <- sin(pi/4) C <- cos(pi/3) T <- tan(pi/4)

print( c( asin(S), asind(S) ) ) print( c( acos(C), acosd(C) ) ) print( c( atan(T), atand(T) ) )</lang>

Racket

<lang Racket>#lang racket (define radians (/ pi 4)) (define degrees 45)

(displayln (format "~a ~a" (sin radians) (sin (* degrees (/ pi 180)))))

(displayln (format "~a ~a" (cos radians) (cos (* degrees (/ pi 180)))))

(displayln (format "~a ~a" (tan radians) (tan (* degrees (/ pi 180)))))

(define arcsin (asin (sin radians))) (displayln (format "~a ~a" arcsin (* arcsin (/ 180 pi))))

(define arccos (acos (cos radians))) (displayln (format "~a ~a" arccos (* arccos (/ 180 pi))))

(define arctan (atan (tan radians))) (display (format "~a ~a" arctan (* arctan (/ 180 pi))))</lang>

RapidQ

<lang RapidQ>$APPTYPE CONSOLE $TYPECHECK ON

SUB pause(prompt$)

   PRINT prompt$
   DO
       SLEEP .1
   LOOP UNTIL LEN(INKEY$) > 0

END SUB

'MAIN DEFDBL pi , radians , degrees , deg2rad pi = 4 * ATAN(1) deg2rad = pi / 180 radians = pi / 4 degrees = 45 * deg2rad

PRINT format$("%.6n" , SIN(radians)) + " " + format$("%.6n" , SIN(degrees)) PRINT format$("%.6n" , COS(radians)) + " " + format$("%.6n" , COS(degrees)) PRINT format$("%.6n" , TAN(radians)) + " " + format$("%.6n" , TAN(degrees))

DEFDBL temp = SIN(radians) PRINT format$("%.6n" , ASIN(temp)) + " " + format$("%.6n" , ASIN(temp) / deg2rad)

temp = COS(radians) PRINT format$("%.6n" , ACOS(temp)) + " " + format$("%.6n" , ACOS(temp) / deg2rad)

temp = TAN(radians) PRINT format$("%.6n" , ATAN(temp)) + " " + format$("%.6n" , ATAN(temp) / deg2rad)

pause("Press any key to continue.")

END 'MAIN</lang>

REBOL

<lang REBOL>REBOL [ Title: "Trigonometric Functions" Author: oofoe Date: 2009-12-07 URL: http://rosettacode.org/wiki/Trigonometric_Functions ]

radians: pi / 4 degrees: 45.0

Unlike most languages, REBOL's trig functions work in degrees unless
you specify differently.

print [sine/radians radians sine degrees] print [cosine/radians radians cosine degrees] print [tangent/radians radians tangent degrees]

d2r: func [ "Convert degrees to radians." d [number!] "Degrees" ][d * pi / 180]

arcsin: arcsine sine degrees print [d2r arcsin arcsin]

arccos: arccosine cosine degrees print [d2r arccos arccos]

arctan: arctangent tangent degrees print [d2r arctan arctan]</lang>

Output:

0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
1.0 1.0
0.785398163397448 45.0
0.785398163397448 45.0
0.785398163397448 45.0

REXX

The REXX language doesn't have any trig functions (or for that matter, a square root [SQRT] function), so if higher math
functions are wanted, you have to roll your own. Some of the normal/regular trigonometric functions are included here. <lang rexx> ┌──────────────────────────────────────────────────────────────────────────┐

│  One common method that ensures enough accuracy in REXX is specifying    │
│  more precision  (via  NUMERIC DIGITS  nnn)  than is needed,  and then   │
│  displaying the number of digits that are desired,  or  the number(s)    │
│  could be re-normalized using the  FORMAT  BIF.                          │
│                                                                          │
│  The technique used (below) is to set the   numeric digits   ten higher  │ 
│  than the desired digits,  as specified by the   SHOWDIGS  variable.     │
└──────────────────────────────────────────────────────────────────────────┘</lang>

Most math (POW, EXP, LOG, LN, GAMMA, etc.), trigonometric, and hyperbolic functions need only five extra digits, but ten
extra digits is safer in case the argument is close to an asymptotic point or a multiple or fractional part of pi or somesuch.
It should also be noted that both the pi and e constants have only around 77 decimal digits as included here, if more
precision is needed, those constants should be extended. Both pi and e could've been shown with more precision,
but having large precision numbers would add to this REXX program's length. If anybody wishes to see this REXX version of
extended digits for pi or e, I could extend them to any almost any precision (as a REXX constant). Normally, a REXX
(external) subroutine is used for such purposes so as to not make the program using the constant unwieldy large. <lang rexx>/*REXX program demonstrates some common trig functions (30 digits shown)*/ showdigs=30 /*show only 30 digits of number. */ numeric digits showdigs+10 /*DIGITS default is 9, but use */

                                      /*extra digs to prevent rounding.*/

say 'Using' showdigs 'decimal digits precision.'; say

 do j=-180  to +180  by 15            /*let's just do a half-Monty.    */
 stuff = right(j,4)       'degrees, rads='show( d2r(j)),
                                 '   sin='show(sinD(j)),
                                 '   cos='show(cosD(J))
                                           /*don't let  TAN  go postal.*/
 if abs(j)\==90  then stuff=stuff '   tan='show(tanD(j))
 say stuff
 end   /*j*/

say; do k=-1 to +1 by 1/2 /*keep the Arc-functions happy. */

         say right(k,4)   'radians, degs='show( r2d(k)),
                                 '  Acos='show(Acos(k)),
                                 '  Asin='show(Asin(k)),
                                 '  Atan='show(Atan(k))
         end   /*k*/

exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────subroutines─────────────────────────*/ Asin: procedure; parse arg x 1 z 1 o 1 p; a=abs(x); aa=a*a

         if a>1  then call AsinErr x           /*X arg is out of range.*/
         if a>=sqrt(2)*.5  then  return sign(x)*acos(sqrt(1-aa), '-ASIN')
         do j=2 by 2 until p=z;  p=z;  o=o*aa*(j-1)/j;  z=z+o/(j+1);  end
         return  z                      /* [↑]  compute until no noise.*/

Atan: procedure; parse arg x; if abs(x)=1 then return pi() * .25 * sign(x)

                                              return Asin(x/sqrt(1+x*x) )

cos: procedure; parse arg x; x=r2r(x); a=abs(x); hpi=pi*.5

         numeric fuzz min(6,digits()-3);       if a=pi()   then return -1
         if a=hpi | a=hpi*3  then return 0;    if a=pi()/3 then return .5
         if a=pi()*2/3  then return -.5;             return .sinCos(1,-1)

sin: procedure; parse arg x; x=r2r(x); numeric fuzz $fuzz(5, 3)

       if x=pi*.5  then return 1;               if x==pi*1.5  then return -1
       if abs(x)=pi | x=0   then return 0;      return  .sinCos(x,1)

.sinCos: parse arg z 1 _,i; q=x*x

         do k=2  by 2  until p=z;  p=z;  _=-_*q/(k*(k+i));  z=z+_;  end   /*k*/
         return z

sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); i=; m.=9

     numeric digits 9; numeric form; h=d+6;  if x<0  then  do; x=-x; i='i'; end
     parse value format(x,2,1,,0) 'E0'  with  g 'E' _ .;       g=g*.5'e'_%2
        do j=0  while h>9;      m.j=h;              h=h%2+1;         end  /*j*/
        do k=j+5  to 0  by -1;  numeric digits m.k; g=(g+x/g)*.5;    end  /*k*/
     numeric digits d;     return (g/1)i            /*make complex if  X < 0.*/

e: e=2.7182818284590452353602874713526624977572470936999595749669676277240766303535 return e /*Note: the actual E subroutine returns E's accuracy that */

                   /*matches the current NUMERIC DIGITS, up to 1 million digits.*/

exp: procedure; parse arg x; ix=x%1; if abs(x-ix)>.5 then ix=ix+sign(x); x=x-ix

    z=1; _=1; w=z;  do j=1;  _=_*x/j;  z=(z+_)/1;  if z==w  then leave; w=z;  end
    if z\==0  then z=e()**ix*z;        return z

pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862 return pi /*Note: the actual PI subroutine returns PI's accuracy that */

                     /*matches the current NUMERIC DIGITS, up to 1 million digits.*/
                     /*John Machin's formula is used for calculating more digits. */

$fuzz: return min(arg(1), max(1, digits() - arg(2) ) ) Acos: procedure; parse arg x; if x<-1|x>1 then call AcosErr; return pi()*.5-Asin(x) AcosD: return r2d(Acos(arg(1))) AsinD: return r2d(Asin(arg(1))) cosD: return cos(d2r(arg(1))) sinD: return sin(d2r(d2d(arg(1)))) tan: procedure; parse arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_ tanD: return tan(d2r(arg(1))) d2d: return arg(1) // 360 /*normalize degrees ──► a unit circle*/ d2r: return r2r(d2d(arg(1))*pi() / 180) /*convert degrees ──► radians. */ r2d: return d2d((arg(1)*180 / pi())) /*convert radians ──► degrees. */ r2r: return arg(1) // (pi()*2) /*normalize radians ──► a unit circle*/ show: return left(left(,arg(1)>=0)format(arg(1),,showdigs)/1,showdigs) tellErr: say; say '*** error! ***'; say; say arg(1); say; exit 13 tanErr: call tellErr 'tan(' || x") causes division by zero, X=" || x AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' || x AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' || x</lang> Programming note: <lang rexx> ╔═════════════════════════════════════════════════════════════════════════════╗

║ Functions that are not included here are   (among others):                  ║
║                                                                             ║
║ some of the usual higher-math functions normally associated with trig       ║
║ functions:             POW, GAMMA, LGGAMMA,  ERF, ERFC,  ROOT,  ATAN2,      ║
║                        LOG (LN),   LOG2,   LOG10,      and all of the       ║
║ hyperbolic trigonometric functions  and  their  inverses  (too many to list ║
║                        here),                                               ║
║ angle conversions/normalizations:  degrees/radians/grads/mils:              ║
║     a circle  ≡  2 pi radians  ≡  360 degrees  ≡  400 grads  ≡  6400 mils.  ║
║                                                                             ║
║ Some of the other trigonometric functions are (hyphens added intentionally):║
║                                                                             ║
║     CHORD                                                                   ║
║     COT    (co-tangent)                                                     ║
║     CSC    (co-secant)                                                      ║
║     CVC    (co-versed cosine)                                               ║
║     CVS    (co-versed sine)                                                 ║
║     CXS    (co-exsecant)                                                    ║
║     HAC    (haver-cosine)                                                   ║
║     HAV    (haver-sine                                                      ║
║     SEC    (secant)                                                         ║
║     VCS    (versed cosine or ver-cosine)                                    ║
║     VSN    (versed sine   or ver-sine)                                      ║
║     XCS    (ex-secant)                                                      ║
║     COS/SIN/TAN cardinal  (damped  COS/SIN/TAN  functions)                  ║
║     COS/SIN     integral                                                    ║
║                                                                             ║
║       and all pertinent inverses of the above functions  (AVSN, ACVS, ···). ║
╚═════════════════════════════════════════════════════════════════════════════╝</lang>

output

Using 30 decimal digits precision.

-180 degrees, rads=-3.141592653589793238462643383    sin= 0                                cos=-1                                tan= 0
-165 degrees, rads=-2.879793265790643801924089768    sin=-0.258819045102520762348898837    cos=-0.965925826289068286749743199    tan= 0.267949192431122706472553658
-150 degrees, rads=-2.617993877991494365385536152    sin=-0.5                              cos=-0.866025403784438646763723170    tan= 0.577350269189625764509148780
-135 degrees, rads=-2.356194490192344928846982537    sin=-0.707106781186547524400844362    cos=-0.707106781186547524400844362    tan= 1
-120 degrees, rads=-2.094395102393195492308428922    sin=-0.866025403784438646763723170    cos=-0.5                              tan= 1.732050807568877293527446341
-105 degrees, rads=-1.832595714594046055769875306    sin=-0.965925826289068286749743199    cos=-0.258819045102520762348898837    tan= 3.732050807568877293527446341
 -90 degrees, rads=-1.570796326794896619231321691    sin=-1                                cos= 0
 -75 degrees, rads=-1.308996938995747182692768076    sin=-0.965925826289068286749743199    cos= 0.258819045102520762348898837    tan=-3.732050807568877293527446341
 -60 degrees, rads=-1.047197551196597746154214461    sin=-0.866025403784438646763723170    cos= 0.5                              tan=-1.732050807568877293527446341
 -45 degrees, rads=-0.785398163397448309615660845    sin=-0.707106781186547524400844362    cos= 0.707106781186547524400844362    tan=-1
 -30 degrees, rads=-0.523598775598298873077107230    sin=-0.5                              cos= 0.866025403784438646763723170    tan=-0.577350269189625764509148780
 -15 degrees, rads=-0.261799387799149436538553615    sin=-0.258819045102520762348898837    cos= 0.965925826289068286749743199    tan=-0.267949192431122706472553658
   0 degrees, rads= 0                                sin= 0                                cos= 1                                tan= 0
  15 degrees, rads= 0.261799387799149436538553615    sin= 0.258819045102520762348898837    cos= 0.965925826289068286749743199    tan= 0.267949192431122706472553658
  30 degrees, rads= 0.523598775598298873077107230    sin= 0.5                              cos= 0.866025403784438646763723170    tan= 0.577350269189625764509148780
  45 degrees, rads= 0.785398163397448309615660845    sin= 0.707106781186547524400844362    cos= 0.707106781186547524400844362    tan= 1
  60 degrees, rads= 1.047197551196597746154214461    sin= 0.866025403784438646763723170    cos= 0.5                              tan= 1.732050807568877293527446341
  75 degrees, rads= 1.308996938995747182692768076    sin= 0.965925826289068286749743199    cos= 0.258819045102520762348898837    tan= 3.732050807568877293527446341
  90 degrees, rads= 1.570796326794896619231321691    sin= 1                                cos= 0
 105 degrees, rads= 1.832595714594046055769875306    sin= 0.965925826289068286749743199    cos=-0.258819045102520762348898837    tan=-3.732050807568877293527446341
 120 degrees, rads= 2.094395102393195492308428922    sin= 0.866025403784438646763723170    cos=-0.5                              tan=-1.732050807568877293527446341
 135 degrees, rads= 2.356194490192344928846982537    sin= 0.707106781186547524400844362    cos=-0.707106781186547524400844362    tan=-1
 150 degrees, rads= 2.617993877991494365385536152    sin= 0.5                              cos=-0.866025403784438646763723170    tan=-0.577350269189625764509148780
 165 degrees, rads= 2.879793265790643801924089768    sin= 0.258819045102520762348898837    cos=-0.965925826289068286749743199    tan=-0.267949192431122706472553658
 180 degrees, rads= 3.141592653589793238462643383    sin= 0                                cos=-1                                tan= 0

  -1 radians, degs=-57.29577951308232087679815481   Acos= 3.141592653589793238462643383   Asin=-1.570796326794896619231321691   Atan=-0.785398163397448309615660845
-0.5 radians, degs=-28.64788975654116043839907740   Acos= 2.094395102393195492308428922   Asin=-0.523598775598298873077107230   Atan=-0.463647609000806116214256231
   0 radians, degs= 0                               Acos= 1.570796326794896619231321691   Asin= 0                               Atan= 0
 0.5 radians, degs= 28.64788975654116043839907740   Acos= 1.047197551196597746154214461   Asin= 0.523598775598298873077107230   Atan= 0.463647609000806116214256231
 1.0 radians, degs= 57.29577951308232087679815481   Acos= 0                               Asin= 1.570796326794896619231321691   Atan= 0.785398163397448309615660845

Ruby

Ruby's Math module contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees.

<lang ruby>radians = Math::PI / 4 degrees = 45.0

def deg2rad(d)

 d * Math::PI / 180

end

def rad2deg(r)

 r * 180 / Math::PI

end

sine

puts "#{Math.sin(radians)} #{Math.sin(deg2rad(degrees))}"

cosine

puts "#{Math.cos(radians)} #{Math.cos(deg2rad(degrees))}"

tangent

puts "#{Math.tan(radians)} #{Math.tan(deg2rad(degrees))}"

arcsine

arcsin = Math.asin(Math.sin(radians)) puts "#{arcsin} #{rad2deg(arcsin)}"

arccosine

arccos = Math.acos(Math.cos(radians)) puts "#{arccos} #{rad2deg(arccos)}"

arctangent

arctan = Math.atan(Math.tan(radians)) puts "#{arctan} #{rad2deg(arctan)}"</lang>

Output:

0.7071067811865475 0.7071067811865475
0.7071067811865476 0.7071067811865476
0.9999999999999999 0.9999999999999999
0.7853981633974482 44.99999999999999
0.7853981633974483 45.0
0.7853981633974483 45.0

BigDecimal

If you want more digits in the answer, then you can use the BigDecimal class. BigMath only has big versions of sine, cosine, and arctangent; so we must implement tangent, arcsine and arccosine.

Translation of: bc

Works with: Ruby version 1.9

<lang ruby>require 'bigdecimal' # BigDecimal require 'bigdecimal/math' # BigMath

include BigMath # Allow sin(x, prec) instead of BigMath.sin(x, prec).

Tangent of _x_.

def tan(x, prec)

 sin(x, prec) / cos(x, prec)

end

Arcsine of _y_, domain [-1, 1], range [-pi/2, pi/2].

def asin(y, prec)

 # Handle angles with no tangent.
 return -PI / 2 if y == -1
 return PI / 2 if y == 1
 
 # Tangent of angle is y / x, where x^2 + y^2 = 1.
 atan(y / sqrt(1 - y * y, prec), prec)

end

Arccosine of _x_, domain [-1, 1], range [0, pi].

def acos(x, prec)

 # Handle angle with no tangent.
 return PI / 2 if x == 0
 
 # Tangent of angle is y / x, where x^2 + y^2 = 1.
 a = atan(sqrt(1 - x * x, prec) / x, prec)
 if a < 0
   a + PI(prec)
 else
   a
 end

end

prec = 52 pi = PI(prec) degrees = pi / 180 # one degree in radians

b1 = BigDecimal.new "1" b2 = BigDecimal.new "2" b3 = BigDecimal.new "3"

f = proc { |big| big.round(50).to_s('F') } print("Using radians:",

     "\n  sin(-pi / 6) = ", f[ sin(-pi / 6, prec) ],
     "\n  cos(3 * pi / 4) = ", f[ cos(3 * pi / 4, prec) ],
     "\n  tan(pi / 3) = ", f[ tan(pi / 3, prec) ],
     "\n  asin(-1 / 2) = ", f[ asin(-b1 / 2, prec) ],
     "\n  acos(-sqrt(2) / 2) = ", f[ acos(-sqrt(b2, prec) / 2, prec) ],
     "\n  atan(sqrt(3)) = ", f[ atan(sqrt(b3, prec), prec) ],
     "\n")

print("Using degrees:",

     "\n  sin(-30) = ", f[ sin(-30 * degrees, prec) ],
     "\n  cos(135) = ", f[ cos(135 * degrees, prec) ],
     "\n  tan(60) = ", f[ tan(60 * degrees, prec) ],
     "\n  asin(-1 / 2) = ",
     f[ asin(-b1 / 2, prec) / degrees ],
     "\n  acos(-sqrt(2) / 2) = ",
     f[ acos(-sqrt(b2, prec) / 2, prec) / degrees ],
     "\n  atan(sqrt(3)) = ",
     f[ atan(sqrt(b3, prec), prec) / degrees ],
     "\n")</lang>

Output:

Using radians:
  sin(-pi / 6) = -0.5
  cos(3 * pi / 4) = -0.70710678118654752440084436210484903928483593768847
  tan(pi / 3) = 1.73205080756887729352744634150587236694280525381038
  asin(-1 / 2) = -0.52359877559829887307710723054658381403286156656252
  acos(-sqrt(2) / 2) = 2.35619449019234492884698253745962716314787704953133
  atan(sqrt(3)) = 1.04719755119659774615421446109316762806572313312504
Using degrees:
  sin(-30) = -0.5
  cos(135) = -0.70710678118654752440084436210484903928483593768847
  tan(60) = 1.73205080756887729352744634150587236694280525381038
  asin(-1 / 2) = -30.0
  acos(-sqrt(2) / 2) = 135.0
  atan(sqrt(3)) = 60.0

Run BASIC

<lang runbasic>' Find these three ratios: Sine, Cosine, Tangent. (These ratios have NO units.)

deg = 45.0 ' Run BASIC works in radians; so, first convert deg to rad as shown in next line. rad = deg * (atn(1)/45) print "Ratios for a "; deg; " degree angle, (or "; rad; " radian angle.)" print "Sine: "; SIN(rad) print "Cosine: "; COS(rad) print "Tangent: "; TAN(rad)

print "Inverse Functions - - (Using above ratios)" ' Now, use those ratios to work backwards to show their original angle in radians. ' Also, use this: rad / (atn(1)/45) = deg (To change radians to degrees.) print "Arcsine: "; ASN(SIN(rad)); " radians, (or "; ASN(SIN(rad))/(atn(1)/45); " degrees)" print "Arccosine: "; ACS(COS(rad)); " radians, (or "; ACS(COS(rad))/(atn(1)/45); " degrees)" print "Arctangent: "; ATN(TAN(rad)); " radians, (or "; ATN(TAN(rad))/(atn(1)/45); " degrees)"

' This code also works in Liberty BASIC. ' The above (atn(1)/45) = approx .01745329252</lang>

Output:

Ratios for a 45.0 degree angle, (or 0.785398163 radian angle.)
Sine:        0.707106781
Cosine:      0.707106781
Tangent:     1.0
Inverse Functions - - (Using above ratios)
Arcsine:     0.785398163 radians, (or 45.0 degrees)
Arccosine:   0.785398163 radians, (or 45.0 degrees)
Arctangent:  0.785398163 radians, (or 45.0 degrees)

SAS

<lang sas>data _null_; pi = 4*atan(1); deg = 30; rad = pi/6; k = pi/180; x = 0.2;

a = sin(rad); b = sin(deg*k); put a b;

a = cos(rad); b = cos(deg*k); put a b;

a = tan(rad); b = tan(deg*k); put a b;

a=arsin(x); b=arsin(x)/k; put a b;

a=arcos(x); b=arcos(x)/k; put a b;

a=atan(x); b=atan(x)/k; put a b; run;</lang>

Scala

Library: Scala

<lang Scala>import scala.math._

object Gonio extends App {

 //Pi / 4 rad is 45 degrees. All answers should be the same.
 val radians = Pi / 4
 val degrees = 45.0

 println(s"${sin(radians)} ${sin(toRadians(degrees))}")
 //cosine
 println(s"${cos(radians)} ${cos(toRadians(degrees))}")
 //tangent
 println(s"${tan(radians)} ${tan(toRadians(degrees))}")
 //arcsine
 val bgsin = asin(sin(radians))
 println(s"$bgsin ${toDegrees(bgsin)}")
 val bgcos = acos(cos(radians))
 println(s"$bgcos ${toDegrees(bgcos)}")
 //arctangent
 val bgtan = atan(tan(radians))
 println(s"$bgtan ${toDegrees(bgtan)}")
 val bgtan2 = atan2(1, 1)
 println(s"$bgtan ${toDegrees(bgtan)}")

}</lang>

Scheme

<lang scheme>(define pi (* 4 (atan 1)))

(define radians (/ pi 4)) (define degrees 45)

(display (sin radians)) (display " ") (display (sin (* degrees (/ pi 180)))) (newline)

(display (cos radians)) (display " ") (display (cos (* degrees (/ pi 180)))) (newline)

(display (tan radians)) (display " ") (display (tan (* degrees (/ pi 180)))) (newline)

(define arcsin (asin (sin radians))) (display arcsin) (display " ") (display (* arcsin (/ 180 pi))) (newline)

(define arccos (acos (cos radians))) (display arccos) (display " ") (display (* arccos (/ 180 pi))) (newline)

(define arctan (atan (tan radians))) (display arctan) (display " ") (display (* arctan (/ 180 pi))) (newline)</lang>

Seed7

The example below uses the libaray math.s7i, which defines, besides many other functions, sin, cos, tan, asin, acos and atan.

<lang seed7>$ include "seed7_05.s7i";

 include "float.s7i";
 include "math.s7i";

const proc: main is func

 local
   const float: radians is PI / 4.0;
   const float: degrees is 45.0;
 begin
   writeln("            radians  degrees");
   writeln("sine:       " <& sin(radians) digits 5 <& sin(degrees * PI / 180.0) digits 5 lpad 9);
   writeln("cosine:     " <& cos(radians) digits 5 <& cos(degrees * PI / 180.0) digits 5 lpad 9);
   writeln("tangent:    " <& tan(radians) digits 5 <& tan(degrees * PI / 180.0) digits 5 lpad 9);
   writeln("arcsine:    " <& asin(0.70710677) digits 5 <& asin(0.70710677) * 180.0 / PI digits 5 lpad 9);
   writeln("arccosine:  " <& acos(0.70710677) digits 5 <& acos(0.70710677) * 180.0 / PI digits 5 lpad 9);
   writeln("arctangent: " <& atan(1.0) digits 5 <& atan(1.0) * 180.0 / PI digits 5 lpad 9);
 end func;</lang>

Output:

            radians  degrees
sine:       0.70711  0.70711
cosine:     0.70711  0.70711
tangent:    1.00000  1.00000
arcsine:    0.78540 45.00000
arccosine:  0.78540 45.00000
arctangent: 0.78540 45.00000

Sidef

<lang ruby>var angle_deg = 45; var angle_rad = Math.pi/4;

[

   [Math.sin(angle_rad), Math.sin(Math.deg2rad(angle_deg))],
   [Math.cos(angle_rad), Math.cos(Math.deg2rad(angle_deg))],
   [Math.tan(angle_rad), Math.tan(Math.deg2rad(angle_deg))],
   [Math.cot(angle_rad), Math.cot(Math.deg2rad(angle_deg))],

].each { |arr|

   say arr.join(" ");

}

[

   Math.asin(Math.sin(angle_rad)),
   Math.acos(Math.cos(angle_rad)),
   Math.atan(Math.tan(angle_rad)),
   Math.acot(Math.cot(angle_rad)),

].each { |n|

   say [n, Math.rad2deg(n)].join(" ");

}</lang>

Output:

0.707106781186547 0.707106781186547
0.707106781186548 0.707106781186548
1 1
1 1
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45
0.785398163397448 45

Tcl

The built-in functions only take radian arguments. <lang tcl>package require Tcl 8.5

proc PI {} {expr {4*atan(1)}} proc deg2rad d {expr {$d/180*[PI]}} proc rad2deg r {expr {$r*180/[PI]}}

namespace path ::tcl::mathfunc

proc trig degrees {

   set radians [deg2rad $degrees]
   puts [sin $radians]
   puts [cos $radians]
   puts [tan $radians]
   set arcsin [asin [sin $radians]]; puts "$arcsin [rad2deg $arcsin]"
   set arccos [acos [cos $radians]]; puts "$arccos [rad2deg $arccos]"
   set arctan [atan [tan $radians]]; puts "$arctan [rad2deg $arctan]"

} trig 60.0</lang>

0.8660254037844386
0.5000000000000001
1.7320508075688767
1.0471975511965976 59.99999999999999
1.0471975511965976 59.99999999999999
1.0471975511965976 59.99999999999999

XPL0

<lang XPL0>include c:\cxpl\codes; \intrinsic 'code' declarations def Pi = 3.14159265358979323846;

func real ATan(Y); \Arc tangent real Y; return ATan2(Y, 1.0);

func real Deg(X); \Convert radians to degrees real X; return 57.2957795130823 * X;

func real Rad(X); \Convert degrees to radians real X; return X / 57.2957795130823;

real A, B, C; [A:= Sin(Pi/6.0); RlOut(0, A); ChOut(0, 9\tab\); RlOut(0, Sin(Rad(30.0))); CrLf(0); B:= Cos(Pi/6.0); RlOut(0, B); ChOut(0, 9\tab\); RlOut(0, Cos(Rad(30.0))); CrLf(0); C:= Tan(Pi/4.0); RlOut(0, C); ChOut(0, 9\tab\); RlOut(0, Tan(Rad(45.0))); CrLf(0);

RlOut(0, ASin(A)); ChOut(0, 9\tab\); RlOut(0, Deg(ASin(A))); CrLf(0); RlOut(0, ACos(B)); ChOut(0, 9\tab\); RlOut(0, Deg(ACos(B))); CrLf(0); RlOut(0, ATan(C)); ChOut(0, 9\tab\); RlOut(0, Deg(ATan(C))); CrLf(0); ]</lang>

Output:

    0.50000         0.50000
    0.86603         0.86603
    1.00000         1.00000
    0.52360        30.00000
    0.52360        30.00000
    0.78540        45.00000

zkl

<lang zkl> (30.0).toRad().sin() //-->0.5 (60.0).toRad().cos() //-->0.5 (45.0).toRad().tan() //-->1 (0.523599).sin() //-->0.5 etc

(0.5).asin() //-->0.523599 (0.5).acos() //-->1.0472 (1.0).atan() //-->0.785398 (1.0).atan().toDeg() //-->45 etc</lang>