Cos Method
This documentation is archived and is not being maintained.

Math.Cos Method

Updated: May 2009

Returns the cosine of the specified angle.

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

'Declaration
Public Shared Function Cos ( _
	d As Double _
) As Double
'Usage
Dim d As Double 
Dim returnValue As Double 

returnValue = Math.Cos(d)

Parameters

d
Type: System.Double

An angle, measured in radians.

Return Value

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

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.

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. 
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

Windows 7, Windows Vista, Windows XP SP2, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP Starter Edition, Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows Server 2000 SP4, Windows Millennium Edition, Windows 98, Windows CE, Windows Mobile for Smartphone, Windows Mobile for Pocket PC, Xbox 360, Zune

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

.NET Framework

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

.NET Compact Framework

Supported in: 3.5, 2.0, 1.0

XNA Framework

Supported in: 3.0, 2.0, 1.0

Date

History

Reason

May 2009

Added information about the return value.

Customer feedback.

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