Trigonometric functions
You are encouraged to solve this task according to the task description, using any language you may know.
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.
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
<lang algol> 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
AWK
awk provides just these bare necessities for trigonometry:
$ awk 'BEGIN{p4=3.14159/4;print cos(p4),sin(p4),atan2(1,1)}'
0.707107 0.707106 0.785398
BASIC
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 arcsin = 2 * ATN(SIN(radians)) * radians / (1 + SQR(1 - radians ^ 2)) PRINT arcsin + " " + arcsin * 180 / pi 'arccos arccos = 2 * ATN(COS(radians)) * SQR(1 - radians ^ 2) / (1 + radians) PRINT arccos + " " + arccos * 180 / pi PRINT ATN(TAN(radians)) + " " + ATN(TAN(radians)) * 180 / pi 'arctan </lang>
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>
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
<lang d> import std.stdio, std.math ;
int main() {
double Pi = 4.0 * atan(1.0); // in D math module, PI is a _real_ constant of p
/*Pi / 4 is 45 degrees. All answers should be the same.*/
double radians = Pi / 4.0;
double degrees = 45.0;
double temp;
/*sine*/
writef("%f %f\n", sin(radians), sin(degrees * Pi / 180.0));
/*cosine*/
writef("%f %f\n", cos(radians), cos(degrees * Pi / 180.0));
/*tangent*/
writef("%f %f\n", tan(radians), tan(degrees * Pi / 180.0));
/*arcsine*/
temp = asin(sin(radians));
writef("%f %f\n", temp, temp * 180.0 / Pi);
/*arccosine*/
temp = acos(cos(radians));
writef("%f %f\n", temp, temp * 180.0 / Pi);
/*arctangent*/
temp = atan(tan(radians));
writef("%f %f\n", temp, temp * 180.0 / Pi);
return 0;
} </lang>
E
<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
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>
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>
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>
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</lang>
0.707107 0.707107
0.707107 0.707107
1 1
Arcsine, arccosine, and arctangent of one-half, in radians and degrees: <lang j> >,:([ , 180p_1&*)&.> (_1&o. ; _2&o. ; _3&o.) 0.5</lang>
0.523599 30 1.0472 60 0.463648 26.5651
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> //Pi / 4 is 45 degrees. All answers should be the same. var radians = Math.PI / 4; var degrees = 45.0; //sine window.alert(Math.sin(radians) + " " + Math.sin(degrees * Math.PI / 180)); //cosine window.alert(Math.cos(radians) + " " + Math.cos(degrees * Math.PI / 180)); //tangent window.alert(Math.tan(radians) + " " + Math.tan(degrees * Math.PI / 180)); //arcsine var arcsin = Math.asin(Math.sin(radians)); window.alert(arcsin + " " + (arcsin * 180 / Math.PI)); //arccosine var arccos = Math.acos(Math.cos(radians)); window.alert(arccos + " " + (arccos * 180 / Math.PI)); //arctangent var arctan = Math.atan(Math.tan(radians)); window.alert(arctan + " " + (arctan * 180 / Math.PI)); </lang>
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>
MAXScript
Maxscript trigonometric functions accept degrees only. The built-ins degToRad and radToDeg allow easy conversion.
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))
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>
OCaml
OCaml's preloaded Pervasives modules 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)
Perl
<lang perl> use Math::Trig;
$angle_degrees = 45; $angle_radians = pi / 4;
print sin($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"; $asin = asin(sin($angle_radians)); print $asin.' '.rad2deg($asin)."\n"; $acos = acos(cos($angle_radians)); print $acos.' '.rad2deg($acos)."\n"; $atan = atan(tan($angle_radians)); print $atan.' '.rad2deg($atan)."\n"; $acot = acot(cot($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
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>
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> import math
radians = math.pi / 4 degrees = 45.0
- sine
print math.sin(radians), math.sin(math.radians(degrees))
- cosine
print math.cos(radians), math.cos(math.radians(degrees))
- tangent
print math.tan(radians), math.tan(math.radians(degrees))
- arcsine
arcsin = math.asin(math.sin(radians)) print arcsin, math.degrees(arcsin)
- arccosine
arccos = math.acos(math.cos(radians)) print arccos, math.degrees(arccos)
- arctangent
arctan = math.atan(math.tan(radians)) print arctan, math.degrees(arctan) </lang>
Output:
0.707106781187 0.707106781187 0.707106781187 0.707106781187 1.0 1.0 0.785398163397 45.0 0.785398163397 45.0 0.785398163397 45.0
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:
0.707106781187 0.707106781187 0.707106781187 0.707106781187 1.0 1.0 0.785398163397 45.0 0.785398163397 45.0 0.785398163397 45.0
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>
Tcl
The 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