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# Math.Sinh Method

.NET Framework 4.5

Returns the hyperbolic sine of the specified angle.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)
```'Declaration
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.

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

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.
Imports System
Imports Microsoft.VisualBasic

Module SinhCosh

Sub Main()
Console.WriteLine( _
"This example of hyperbolic " & _
"Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
"generates the following output." & vbCrLf)
Console.WriteLine( _
"Evaluate these hyperbolic identities " & _
"with selected values for X:")
Console.WriteLine( _
"   cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
"   sinh(2 * X) = 2 * sinh(X) * cosh(X)")
Console.WriteLine("   cosh(2 * X) = cosh^2(X) + sinh^2(X)")

UseSinhCosh(0.1)
UseSinhCosh(1.2)
UseSinhCosh(4.9)

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

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

' Evaluate hyperbolic identities with a given argument.
Sub UseSinhCosh(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.
Console.WriteLine( _
vbCrLf & "                         Math.Sinh({0}) = {1:E16}" + _
vbCrLf & "                         Math.Cosh({0}) = {2:E16}", _
arg, Math.Sinh(arg), Math.Cosh(arg))
Console.WriteLine( _
"(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 = {1:E16}", _
arg, coshArg * coshArg - sinhArg * sinhArg)

' Evaluate sinh(2 * X) = 2 * sinh(X) * cosh(X).
Console.WriteLine( _
"                         Math.Sinh({0}) = {1:E16}", _
2.0 * arg, Math.Sinh((2.0 * arg)))
Console.WriteLine( _
"    2 * Math.Sinh({0}) * Math.Cosh({0}) = {1:E16}", _
arg, 2.0 * sinhArg * coshArg)

' Evaluate cosh(2 * X) = cosh^2(X) + sinh^2(X).
Console.WriteLine( _
"                         Math.Cosh({0}) = {1:E16}", _
2.0 * arg, Math.Cosh((2.0 * arg)))
Console.WriteLine( _
"(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 = {1:E16}", _
arg, coshArg * coshArg + sinhArg * sinhArg)

End Sub 'UseSinhCosh

' Evaluate hyperbolic identities that are functions of two arguments.
Sub UseTwoArgs(argX As Double, argY As Double)

' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
Console.WriteLine( _
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))
Console.WriteLine( _
"                         Math.Sinh({0}) = {1:E16}", _
argX + argY, Math.Sinh((argX + argY)))

' Evaluate cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
Console.WriteLine( _
"        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))
Console.WriteLine( _
"                         Math.Cosh({0}) = {1:E16}", _
argX + argY, Math.Cosh((argX + argY)))

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
```

#### .NET Framework

Supported in: 4.5.1, 4.5, 4, 3.5, 3.0, 2.0, 1.1, 1.0

#### .NET Framework Client Profile

Supported in: 4, 3.5 SP1

#### Portable Class Library

Supported in: Portable Class Library

#### .NET for Windows Store apps

Supported in: Windows 8

#### .NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone 8, Silverlight 8.1

Windows Phone 8.1, Windows Phone 8, Windows 8.1, Windows Server 2012 R2, Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)

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

#### Reference

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