# Math.Sin Method

Silverlight

Returns the sine of the specified angle.

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

## Syntax

```'Declaration
<SecuritySafeCriticalAttribute> _
Public Shared Function Sin ( _
a As Double _
) As Double
```

#### Parameters

a
Type: System.Double

#### Return Value

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

## Remarks

The angle, a, 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 of this range, the Sin method returns d unchanged rather than throwing an exception.

### Platform Notes

Silverlight for Windows Phone

The value of Math.Sin(Math.PI/2) is 0.99999999999999989. The value on Windows is 1.

## Examples

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.

Module Example

Public Sub Demo(ByVal outputBlock As System.Windows.Controls.TextBlock)
outputBlock.Text &= _
"This example of trigonometric " & _
"Math.Sin( double ) and Math.Cos( double )" & vbCrLf & _
"generates the following output." & vbCrLf & vbCrLf
outputBlock.Text &= _
"Convert selected values for X to radians " & vbCrLf & _
"and evaluate these trigonometric identities:" & vbCrLf
outputBlock.Text &= _
"   sin^2(X) + cos^2(X) = 1" & vbCrLf & _
"   sin(2 * X) = 2 * sin(X) * cos(X)" & vbCrLf
outputBlock.Text &= "   cos(2 * X) = cos^2(X) - sin^2(X)" & vbCrLf

UseSineCosine(outputBlock, 15.0)
UseSineCosine(outputBlock, 30.0)
UseSineCosine(outputBlock, 45.0)

outputBlock.Text &= _
vbCrLf & "Convert selected values for X and Y to radians" & _
vbCrLf & "and evaluate these trigonometric identities:" & vbCrLf
outputBlock.Text &= "   sin(X + Y) = sin(X) * cos(Y) + cos(X) * sin(Y)" & vbCrLf
outputBlock.Text &= "   cos(X + Y) = cos(X) * cos(Y) - sin(X) * sin(Y)" & vbCrLf

UseTwoAngles(outputBlock, 15.0, 30.0)
UseTwoAngles(outputBlock, 30.0, 45.0)
End Sub 'Main

' Evaluate trigonometric identities with a given angle.
Sub UseSineCosine(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal 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.
outputBlock.Text &= String.Format( _
vbCrLf & "                           Math.Sin({0} deg) = {1:E16}" & _
vbCrLf & "                           Math.Cos({0} deg) = {2:E16}", _
degrees, Math.Sin(angle), Math.Cos(angle)) & vbCrLf
outputBlock.Text &= String.Format( _
"(Math.Sin({0} deg))^2 + (Math.Cos({0} deg))^2 = {1:E16}", _
degrees, sinAngle * sinAngle + cosAngle * cosAngle) & vbCrLf

' Evaluate sin(2 * X) = 2 * sin(X) * cos(X).
outputBlock.Text &= String.Format( _
"                           Math.Sin({0} deg) = {1:E16}", _
2.0 * degrees, Math.Sin(2.0 * angle)) & vbCrLf
outputBlock.Text &= String.Format( _
"    2 * Math.Sin({0} deg) * Math.Cos({0} deg) = {1:E16}", _
degrees, 2.0 * sinAngle * cosAngle) & vbCrLf

' Evaluate cos(2 * X) = cos^2(X) - sin^2(X).
outputBlock.Text &= String.Format( _
"                           Math.Cos({0} deg) = {1:E16}", _
2.0 * degrees, Math.Cos(2.0 * angle)) & vbCrLf
outputBlock.Text &= String.Format( _
"(Math.Cos({0} deg))^2 - (Math.Sin({0} deg))^2 = {1:E16}", _
degrees, cosAngle * cosAngle - sinAngle * sinAngle) & vbCrLf

End Sub 'UseSineCosine

' Evaluate trigonometric identities that are functions of two angles.
Sub UseTwoAngles(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal degreesX As Double, ByVal 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).
outputBlock.Text &= String.Format( _
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)) & vbCrLf
outputBlock.Text &= String.Format( _
"                           Math.Sin({0} deg) = {1:E16}", _
degreesX + degreesY, Math.Sin(angleX + angleY)) & vbCrLf

' Evaluate cos(X + Y) = cos(X) * cos(Y) - sin(X) * sin(Y).
outputBlock.Text &= String.Format( _
"        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)) & vbCrLf
outputBlock.Text &= String.Format( _
"                           Math.Cos({0} deg) = {1:E16}", _
degreesX + degreesY, Math.Cos(angleX + angleY)) & vbCrLf

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

```

## Version Information

#### Silverlight

Supported in: 5, 4, 3

#### Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

#### XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

## Platforms

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.