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Math::Sin Method

Returns the sine of the specified angle.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)

public:
static double Sin(
	double a
)

Parameters

a
Type: System::Double

An angle, measured in radians.

Return Value

Type: System::Double
The sine of a. If a is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

The angle, a, must be in radians. Multiply by Math::PI/180 to convert degrees to radians.

Acceptable values of a range from approximately -9223372036854775295 to approximately 9223372036854775295. For values outside of this range, the Sin method returns a unchanged rather than throwing an exception.

The following example uses Sin to evaluate certain trigonometric identities for selected angles.

// Example for the trigonometric Math.Sin( double )  
// and Math.Cos( double ) methods. 
using namespace System;

// Evaluate trigonometric identities with a given angle. 
void UseSineCosine( double degrees )
{
   double angle = Math::PI * degrees / 180.0;
   double sinAngle = Math::Sin( angle );
   double cosAngle = Math::Cos( angle );

   // Evaluate sin^2(X) + cos^2(X) == 1.
   Console::WriteLine( "\n                            Math::Sin({0} deg) == {1:E16}\n" 
   "                            Math::Cos({0} deg) == {2:E16}", degrees, Math::Sin( angle ), Math::Cos( angle ) );
   Console::WriteLine( "(Math::Sin({0} deg))^2 + (Math::Cos({0} deg))^2 == {1:E16}", degrees, sinAngle * sinAngle + cosAngle * cosAngle );

   // Evaluate sin(2 * X) == 2 * sin(X) * cos(X).
   Console::WriteLine( "                            Math::Sin({0} deg) == {1:E16}", 2.0 * degrees, Math::Sin( 2.0 * angle ) );
   Console::WriteLine( "    2 * Math::Sin({0} deg) * Math::Cos({0} deg) == {1:E16}", degrees, 2.0 * sinAngle * cosAngle );

   // Evaluate cos(2 * X) == cos^2(X) - sin^2(X).
   Console::WriteLine( "                            Math::Cos({0} deg) == {1:E16}", 2.0 * degrees, Math::Cos( 2.0 * angle ) );
   Console::WriteLine( "(Math::Cos({0} deg))^2 - (Math::Sin({0} deg))^2 == {1:E16}", degrees, cosAngle * cosAngle - sinAngle * sinAngle );
}


// Evaluate trigonometric identities that are functions of two angles. 
void UseTwoAngles( double degreesX, double degreesY )
{
   double angleX = Math::PI * degreesX / 180.0;
   double angleY = Math::PI * degreesY / 180.0;

   // Evaluate sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y).
   Console::WriteLine( "\n        Math::Sin({0} deg) * Math::Cos({1} deg) +\n" 
   "        Math::Cos({0} deg) * Math::Sin({1} deg) == {2:E16}", degreesX, degreesY, Math::Sin( angleX ) * Math::Cos( angleY ) + Math::Cos( angleX ) * Math::Sin( angleY ) );
   Console::WriteLine( "                            Math::Sin({0} deg) == {1:E16}", degreesX + degreesY, Math::Sin( angleX + angleY ) );

   // Evaluate cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y).
   Console::WriteLine( "        Math::Cos({0} deg) * Math::Cos({1} deg) -\n" 
   "        Math::Sin({0} deg) * Math::Sin({1} deg) == {2:E16}", degreesX, degreesY, Math::Cos( angleX ) * Math::Cos( angleY ) - Math::Sin( angleX ) * Math::Sin( angleY ) );
   Console::WriteLine( "                            Math::Cos({0} deg) == {1:E16}", degreesX + degreesY, Math::Cos( angleX + angleY ) );
}

int main()
{
   Console::WriteLine( "This example of trigonometric " 
   "Math::Sin( double ) and Math::Cos( double )\n" 
   "generates the following output.\n" );
   Console::WriteLine( "Convert selected values for X to radians \n" 
   "and evaluate these trigonometric identities:" );
   Console::WriteLine( "   sin^2(X) + cos^2(X) == 1\n" 
   "   sin(2 * X) == 2 * sin(X) * cos(X)" );
   Console::WriteLine( "   cos(2 * X) == cos^2(X) - sin^2(X)" );
   UseSineCosine( 15.0 );
   UseSineCosine( 30.0 );
   UseSineCosine( 45.0 );
   Console::WriteLine( "\nConvert selected values for X and Y to radians \n" 
   "and evaluate these trigonometric identities:" );
   Console::WriteLine( "   sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y)" );
   Console::WriteLine( "   cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y)" );
   UseTwoAngles( 15.0, 30.0 );
   UseTwoAngles( 30.0, 45.0 );
}

/*
This example of trigonometric Math::Sin( double ) and Math::Cos( double )
generates the following output.

Convert selected values for X to radians
and evaluate these trigonometric identities:
   sin^2(X) + cos^2(X) == 1
   sin(2 * X) == 2 * sin(X) * cos(X)
   cos(2 * X) == cos^2(X) - sin^2(X)

                            Math::Sin(15 deg) == 2.5881904510252074E-001
                            Math::Cos(15 deg) == 9.6592582628906831E-001
(Math::Sin(15 deg))^2 + (Math::Cos(15 deg))^2 == 1.0000000000000000E+000
                            Math::Sin(30 deg) == 4.9999999999999994E-001
    2 * Math::Sin(15 deg) * Math::Cos(15 deg) == 4.9999999999999994E-001
                            Math::Cos(30 deg) == 8.6602540378443871E-001
(Math::Cos(15 deg))^2 - (Math::Sin(15 deg))^2 == 8.6602540378443871E-001

                            Math::Sin(30 deg) == 4.9999999999999994E-001
                            Math::Cos(30 deg) == 8.6602540378443871E-001
(Math::Sin(30 deg))^2 + (Math::Cos(30 deg))^2 == 1.0000000000000000E+000
                            Math::Sin(60 deg) == 8.6602540378443860E-001
    2 * Math::Sin(30 deg) * Math::Cos(30 deg) == 8.6602540378443860E-001
                            Math::Cos(60 deg) == 5.0000000000000011E-001
(Math::Cos(30 deg))^2 - (Math::Sin(30 deg))^2 == 5.0000000000000022E-001

                            Math::Sin(45 deg) == 7.0710678118654746E-001
                            Math::Cos(45 deg) == 7.0710678118654757E-001
(Math::Sin(45 deg))^2 + (Math::Cos(45 deg))^2 == 1.0000000000000000E+000
                            Math::Sin(90 deg) == 1.0000000000000000E+000
    2 * Math::Sin(45 deg) * Math::Cos(45 deg) == 1.0000000000000000E+000
                            Math::Cos(90 deg) == 6.1230317691118863E-017
(Math::Cos(45 deg))^2 - (Math::Sin(45 deg))^2 == 2.2204460492503131E-016

Convert selected values for X and Y to radians
and evaluate these trigonometric identities:
   sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y)
   cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y)

        Math::Sin(15 deg) * Math::Cos(30 deg) +
        Math::Cos(15 deg) * Math::Sin(30 deg) == 7.0710678118654746E-001
                            Math::Sin(45 deg) == 7.0710678118654746E-001
        Math::Cos(15 deg) * Math::Cos(30 deg) -
        Math::Sin(15 deg) * Math::Sin(30 deg) == 7.0710678118654757E-001
                            Math::Cos(45 deg) == 7.0710678118654757E-001

        Math::Sin(30 deg) * Math::Cos(45 deg) +
        Math::Cos(30 deg) * Math::Sin(45 deg) == 9.6592582628906831E-001
                            Math::Sin(75 deg) == 9.6592582628906820E-001
        Math::Cos(30 deg) * Math::Cos(45 deg) -
        Math::Sin(30 deg) * Math::Sin(45 deg) == 2.5881904510252085E-001
                            Math::Cos(75 deg) == 2.5881904510252096E-001
*/

.NET Framework

Supported in: 4.5, 4, 3.5, 3.0, 2.0, 1.1, 1.0

.NET Framework Client Profile

Supported in: 4, 3.5 SP1

Portable Class Library

Supported in: Portable Class Library

.NET for Windows Store apps

Supported in: Windows 8

.NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone Silverlight 8.1, Windows Phone Silverlight 8

Windows Phone 8.1, Windows Phone 8, Windows 8.1, Windows Server 2012 R2, Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

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