# Math.Sinh Method

Silverlight

Returns the hyperbolic sine of the specified angle.

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

## Syntax

```'Declaration
<SecuritySafeCriticalAttribute> _
Public Shared Function Sinh ( _
value As Double _
) As Double
```

#### Parameters

value
Type: System.Double
An angle, measured in radians.

#### Return Value

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

## Remarks

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

## Examples

The following example uses Sinh to evaluate certain hyperbolic identities for selected values.

```
' Example for the hyperbolic Math.Sinh( Double ) and Math.Cosh( Double ) methods.

Module Example

Public Sub Demo(ByVal outputBlock As System.Windows.Controls.TextBlock)
outputBlock.Text &= _
"This example of hyperbolic " & _
"Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
"generates the following output." & vbCrLf & vbCrLf
outputBlock.Text &= _
"Evaluate these hyperbolic identities " & _
"with selected values for X:" & vbCrLf
outputBlock.Text &= _
"   cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
"   sinh(2 * X) = 2 * sinh(X) * cosh(X)" & vbCrLf
outputBlock.Text &= "   cosh(2 * X) = cosh^2(X) + sinh^2(X)" & vbCrLf

UseExample(outputBlock, 0.1)
UseExample(outputBlock, 1.2)
UseExample(outputBlock, 4.9)

outputBlock.Text &= _
vbCrLf & "Evaluate these hyperbolic " & _
"identities with selected values for X and Y:" & vbCrLf
outputBlock.Text &= _
"   sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)" & vbCrLf
outputBlock.Text &= _
"   cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)" & vbCrLf

UseTwoArgs(outputBlock, 0.1, 1.2)
UseTwoArgs(outputBlock, 1.2, 4.9)
End Sub 'Main

' Evaluate hyperbolic identities with a given argument.
Sub UseExample(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal arg As Double)
Dim sinhArg As Double = Math.Sinh(arg)
Dim coshArg As Double = Math.Cosh(arg)

' Evaluate cosh^2(X) - sinh^2(X) = 1.
outputBlock.Text &= String.Format( _
vbCrLf & "                         Math.Sinh({0}) = {1:E16}" + _
vbCrLf & "                         Math.Cosh({0}) = {2:E16}", _
arg, Math.Sinh(arg), Math.Cosh(arg)) & vbCrLf
outputBlock.Text &= String.Format( _
"(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 = {1:E16}", _
arg, coshArg * coshArg - sinhArg * sinhArg) & vbCrLf

' Evaluate sinh(2 * X) = 2 * sinh(X) * cosh(X).
outputBlock.Text &= String.Format( _
"                         Math.Sinh({0}) = {1:E16}", _
2.0 * arg, Math.Sinh((2.0 * arg))) & vbCrLf
outputBlock.Text &= String.Format( _
"    2 * Math.Sinh({0}) * Math.Cosh({0}) = {1:E16}", _
arg, 2.0 * sinhArg * coshArg) & vbCrLf

' Evaluate cosh(2 * X) = cosh^2(X) + sinh^2(X).
outputBlock.Text &= String.Format( _
"                         Math.Cosh({0}) = {1:E16}", _
2.0 * arg, Math.Cosh((2.0 * arg))) & vbCrLf
outputBlock.Text &= String.Format( _
"(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 = {1:E16}", _
arg, coshArg * coshArg + sinhArg * sinhArg) & vbCrLf

End Sub 'UseExample

' Evaluate hyperbolic identities that are functions of two arguments.
Sub UseTwoArgs(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal argX As Double, ByVal argY As Double)

' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
outputBlock.Text &= String.Format( _
vbCrLf & "        Math.Sinh({0}) * Math.Cosh({1}) +" + _
vbCrLf & "        Math.Cosh({0}) * Math.Sinh({1}) = {2:E16}", _
argX, argY, Math.Sinh(argX) * Math.Cosh(argY) + _
Math.Cosh(argX) * Math.Sinh(argY)) & vbCrLf
outputBlock.Text &= String.Format( _
"                         Math.Sinh({0}) = {1:E16}", _
argX + argY, Math.Sinh((argX + argY))) & vbCrLf

' Evaluate cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
outputBlock.Text &= String.Format( _
"        Math.Cosh({0}) * Math.Cosh({1}) +" + _
vbCrLf & "        Math.Sinh({0}) * Math.Sinh({1}) = {2:E16}", _
argX, argY, Math.Cosh(argX) * Math.Cosh(argY) + _
Math.Sinh(argX) * Math.Sinh(argY)) & vbCrLf
outputBlock.Text &= String.Format( _
"                         Math.Cosh({0}) = {1:E16}", _
argX + argY, Math.Cosh((argX + argY))) & vbCrLf

End Sub 'UseTwoArgs
End Module 'SinhCosh

' This example of hyperbolic Math.Sinh( Double ) and Math.Cosh( Double )
' generates the following output.
'
' Evaluate these hyperbolic identities with selected values for X:
'    cosh^2(X) - sinh^2(X) = 1
'    sinh(2 * X) = 2 * sinh(X) * cosh(X)
'    cosh(2 * X) = cosh^2(X) + sinh^2(X)
'
'                          Math.Sinh(0.1) = 1.0016675001984403E-001
'                          Math.Cosh(0.1) = 1.0050041680558035E+000
' (Math.Cosh(0.1))^2 - (Math.Sinh(0.1))^2 = 9.9999999999999989E-001
'                          Math.Sinh(0.2) = 2.0133600254109399E-001
'     2 * Math.Sinh(0.1) * Math.Cosh(0.1) = 2.0133600254109396E-001
'                          Math.Cosh(0.2) = 1.0200667556190759E+000
' (Math.Cosh(0.1))^2 + (Math.Sinh(0.1))^2 = 1.0200667556190757E+000
'
'                          Math.Sinh(1.2) = 1.5094613554121725E+000
'                          Math.Cosh(1.2) = 1.8106555673243747E+000
' (Math.Cosh(1.2))^2 - (Math.Sinh(1.2))^2 = 1.0000000000000000E+000
'                          Math.Sinh(2.4) = 5.4662292136760939E+000
'     2 * Math.Sinh(1.2) * Math.Cosh(1.2) = 5.4662292136760939E+000
'                          Math.Cosh(2.4) = 5.5569471669655064E+000
' (Math.Cosh(1.2))^2 + (Math.Sinh(1.2))^2 = 5.5569471669655064E+000
'
'                          Math.Sinh(4.9) = 6.7141166550932297E+001
'                          Math.Cosh(4.9) = 6.7148613134003227E+001
' (Math.Cosh(4.9))^2 - (Math.Sinh(4.9))^2 = 1.0000000000000000E+000
'                          Math.Sinh(9.8) = 9.0168724361884615E+003
'     2 * Math.Sinh(4.9) * Math.Cosh(4.9) = 9.0168724361884615E+003
'                          Math.Cosh(9.8) = 9.0168724916400624E+003
' (Math.Cosh(4.9))^2 + (Math.Sinh(4.9))^2 = 9.0168724916400606E+003
'
' Evaluate these hyperbolic identities with selected values for X and Y:
'    sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)
'    cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)
'
'         Math.Sinh(0.1) * Math.Cosh(1.2) +
'         Math.Cosh(0.1) * Math.Sinh(1.2) = 1.6983824372926155E+000
'                          Math.Sinh(1.3) = 1.6983824372926160E+000
'         Math.Cosh(0.1) * Math.Cosh(1.2) +
'         Math.Sinh(0.1) * Math.Sinh(1.2) = 1.9709142303266281E+000
'                          Math.Cosh(1.3) = 1.9709142303266285E+000
'
'         Math.Sinh(1.2) * Math.Cosh(4.9) +
'         Math.Cosh(1.2) * Math.Sinh(4.9) = 2.2292776360739879E+002
'                          Math.Sinh(6.1) = 2.2292776360739885E+002
'         Math.Cosh(1.2) * Math.Cosh(4.9) +
'         Math.Sinh(1.2) * Math.Sinh(4.9) = 2.2293000647511826E+002
'                          Math.Cosh(6.1) = 2.2293000647511832E+002

```

## 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.