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). <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; </ada>
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
BASIC
QuickBasic 4.5 does not have arcsin and arccos built in. They are defined by identities found here. <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</qbasic>
C
<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;
}</c>
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
D
<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;
}</d>
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] )
Fortran
Trigonometic functions expect arguments in radians so degrees require conversion
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
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
ATAN2(y,x) ! Arctangent(y/x), -pi < result <= +pi SINH(x) ! Hyperbolic sine COSH(x) ! Hyperbolic cosine TANH(x) ! Hyperbolic tangent
Haskell
Trigonometric functions use radians; degrees require conversion.
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)]
IDL
deg = 35 ; arbitrary number of degrees rad = !dtor*deg ; system variables !dtor and !radeg convert between rad and deg
- 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
- the hyperbolic versions exist and behave as expected
print, sinh(rad) ; etc
- outputs
- 0.649572
- 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
- the trig functions behave as expected for complex arguments
x = complex(1,2) print,sin(x)
- outputs
- ( 3.16578, 1.95960)
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:
>,:(1&o. ; 2&o. ; 3&o.) (4%~o. 1), 180%~o. 45 0.707107 0.707107 0.707107 0.707107 1 1
Arcsine, arccosine, and arctangent of one-half, in radians and degrees:
>,:([ , 180p_1&*)&.> (_1&o. ; _2&o. ; _3&o.) 0.5 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.
<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)); }
}</java>
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.
<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)); </javascript>
Logo
UCB Logo has sine, cosine, and arctangent; each having variants for degrees or radians.
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
OCaml
OCaml's preloaded Pervasives modules contains all six functions. The functions all accept radians only, so conversion is necessary when dealing with degrees. <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);;</ocaml> 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
Perl
<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";</perl>
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.
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) =>
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.
<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)</python>
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
<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)</scheme>