# Math.Cos(Double) Method

## Definition

Returns the cosine of the specified angle.

``````public:
static double Cos(double d);``````
``public static double Cos (double d);``
``static member Cos : double -> double``
``Public Shared Function Cos (d As Double) As Double``

d
Double

#### Returns

Double

The cosine of `d`. If `d` is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

## Examples

The following example uses Cos 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
*/
``````
``````// Example for the trigonometric Math.Sin( double )
// and Math.Cos( double ) methods.
using System;

class SinCos
{
public static void Main()
{
Console.WriteLine(
"This example of trigonometric " +
"Math.Sin( double ), Math.Cos( double ), and Math.SinCos( 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)" );
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);

Console.WriteLine(
"\nWhen you have calls to sin(X) and cos(X) they \n" +
"can be replaced with a single call to sincos(x):" );

UseCombinedSineCosine(15.0);
UseCombinedSineCosine(30.0);
UseCombinedSineCosine(45.0);
}

// Evaluate trigonometric identities with a given angle.
static void UseCombinedSineCosine(double degrees)
{
double angle = Math.PI * degrees / 180.0;
(double sinAngle, double cosAngle) = Math.SinCos(angle);

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

// Evaluate trigonometric identities with a given angle.
static 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.
static 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));
}
}

/*
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
*/
``````
``````' Example for the trigonometric Math.Sin( Double ) and Math.Cos( Double ) methods.
Module SinCos

Sub Main()
Console.WriteLine( _
"This example of trigonometric " & _
"Math.Sin( double ) and Math.Cos( double )" & vbCrLf & _
"generates the following output." & vbCrLf)
Console.WriteLine( _
"Convert selected values for X to radians " & vbCrLf & _
"and evaluate these trigonometric identities:")
Console.WriteLine( _
"   sin^2(X) + cos^2(X) = 1" & vbCrLf & _
"   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( _
vbCrLf & "Convert selected values for X and Y to radians" & _
vbCrLf & "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)
End Sub

' Evaluate trigonometric identities with a given angle.
Sub UseSineCosine(degrees As Double)

Dim angle As Double = Math.PI * degrees / 180.0
Dim sinAngle As Double = Math.Sin(angle)
Dim cosAngle As Double = Math.Cos(angle)

' Evaluate sin^2(X) + cos^2(X) = 1.
Console.WriteLine( _
vbCrLf & "                           Math.Sin({0} deg) = {1:E16}" & _
vbCrLf & "                           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)

End Sub

' Evaluate trigonometric identities that are functions of two angles.
Sub UseTwoAngles(degreesX As Double, degreesY As Double)

Dim angleX As Double = Math.PI * degreesX / 180.0
Dim angleY As Double = Math.PI * degreesY / 180.0

' Evaluate sin(X + Y) = sin(X) * cos(Y) + cos(X) * sin(Y).
Console.WriteLine( _
vbCrLf & "        Math.Sin({0} deg) * Math.Cos({1} deg) +" & _
vbCrLf & "        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) -" & vbCrLf & _
"        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))

End Sub
End Module 'SinCos

' 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
``````

## Remarks

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

This method calls into the underlying C runtime, and the exact result or valid input range may differ between different operating systems or architectures.