Trigonometric functions: Difference between revisions
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(→{{header|BASIC}}: Forgot to give ATN an argument and changed for new requirements.) |
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PRINT TAN(radians) + " " + TAN (degrees) 'tangent |
PRINT TAN(radians) + " " + TAN (degrees) 'tangent |
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'arcsin |
'arcsin |
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arcsin = 2 * ATN * radians / (1 + SQR(1 - radians ^ 2)) |
arcsin = 2 * ATN(SIN(radians)) * radians / (1 + SQR(1 - radians ^ 2)) |
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PRINT arcsin + " " + arcsin * 180 / pi |
PRINT arcsin + " " + arcsin * 180 / pi |
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'arccos |
'arccos |
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arccos = 2 * ATN * SQR(1 - radians ^ 2) / (1 + radians) |
arccos = 2 * ATN(COS(radians)) * SQR(1 - radians ^ 2) / (1 + radians) |
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PRINT arccos + " " + arccos * 180 / pi |
PRINT arccos + " " + arccos * 180 / pi |
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PRINT ATN(radians) + " " + ATN |
PRINT ATN(TAN(radians)) + " " + ATN(TAN(radians)) * 180 / pi 'arctan |
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=={{header|Forth}}== |
=={{header|Forth}}== |
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Revision as of 20:52, 9 January 2008
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).
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;
begin
Put(Item => Sin(Angle_Degrees, Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Sin(Angle_Radians, Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => Cos(Angle_Degrees, Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Cos(Angle_Radians, Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => Tan(Angle_Degrees, Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Tan(Angle_Radians, Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => Cot(Angle_Degrees, Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Cot(Angle_Radians, Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => ArcSin(Sin(Angle_Degrees, Degrees_Cycle), Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => ArcSin(Sin(Angle_Radians, Radians_Cycle), Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => Arccos(Cos(Angle_Degrees, Degrees_Cycle), Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Arccos(Cos(Angle_Radians, Radians_Cycle), Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => Arctan(Y => Tan(Angle_Degrees, Degrees_Cycle), Cycle => Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Arctan(Y => Tan(Angle_Radians, Radians_Cycle), Cycle => Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
Put(Item => Arccot(X => Cot(Angle_Degrees, Degrees_Cycle), Cycle => Degrees_Cycle), Aft => 5, Exp => 0);
Put(" ");
Put(Item => Arccot(X => Cot(Angle_Degrees, Degrees_Cycle), Cycle => Radians_Cycle), Aft => 5, Exp => 0);
New_Line;
end Trig;
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
Compiler: QuickBasic 4.5
QuickBasic 4.5 does not have arcsin and arccos built in. They are defined by identities found here.
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
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] )
J
The circle functions in J include trigonometric functions. Native operation is in radians, so results in degrees involves conversion.
Sine, cosine, and tangent of 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 0.5
>,:([ , 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.
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(degrees * Math.PI / 180));
//cosine
System.out.println(Math.cos(radians) + " " + Math.cos(degrees * Math.PI / 180));
//tangent
System.out.println(Math.tan(radians) + " " + Math.tan(degrees * Math.PI / 180));
//arcsine
double arcsin = Math.asin(Math.sin(radians));
System.out.println(arcsin + " " + arcsin * 180 / Math.PI);
//arccosine
double arccos = Math.acos(Math.cos(radians));
System.out.println(arccos + " " + arccos * 180 / Math.PI);
//arctangent
double arctan = Math.atan(Math.tan(radians));
System.out.println(arctan + " " + arctan * 180 / Math.PI);
}
}
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
Perl
Interpreter: Perl 5.8.8
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($angle_degrees))."\n"; print asin($angle_radians).' '.asin(deg2rad($angle_degrees))."\n"; print acos($angle_radians).' '.acos(deg2rad($angle_degrees))."\n"; print atan($angle_radians).' '.atan(deg2rad($angle_degrees))."\n"; print acot($angle_radians).' '.acot(deg2rad($angle_degrees))."\n";
Output:
0.707106781186547 0.707106781186547 0.707106781186548 0.707106781186548 1 1 1 1 0.903339110766513 0.903339110766513 0.667457216028384 0.667457216028384 0.665773750028354 0.665773750028354 0.905022576766543 0.905022576766543