Math.Cos(Double) Math.Cos(Double) Math.Cos(Double) Method

Definition

Returns the cosine of the specified angle.

public:
 static double Cos(double d);
public static double Cos (double d);
Public Shared Function Cos (d As Double) As Double
Parameters
d
Double Double Double

An angle, measured in radians.

Returns

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 ) 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);
    }

    // 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.
Imports System
Imports Microsoft.VisualBasic

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 'Main
      
    ' 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 'UseSineCosine
       
    ' 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 'UseTwoAngles
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.

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

Applies to