# Math.Tanh Method

.NET Framework 4.6 and 4.5

Returns the hyperbolic tangent of the specified angle.

Namespace:  System
Assemblies:   mscorlib (in mscorlib.dll)
System.Runtime.Extensions (in System.Runtime.Extensions.dll)

## Syntax

'Declaration
Public Shared Function Tanh ( _
value As Double _
) As Double

#### Parameters

value
Type: System.Double

#### Return Value

Type: System.Double
The hyperbolic tangent of value. If value is equal to NegativeInfinity, this method returns -1. If value is equal to PositiveInfinity, this method returns 1. If value is equal to NaN, this method returns NaN.

## Remarks

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

## Examples

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

' Example for the hyperbolic Math.Tanh( Double ) method.
Imports System
Imports Microsoft.VisualBasic

Module DemoTanh

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

UseTanh(0.1)
UseTanh(1.2)
UseTanh(4.9)

Console.WriteLine( _
vbCrLf & "Evaluate [tanh(X + Y) == (tanh(X) + " & _
"tanh(Y)) / (1 + tanh(X) * tanh(Y))]" & _
vbCrLf & "with selected values for X and Y:")

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

' Evaluate hyperbolic identities with a given argument.
Sub UseTanh(arg As Double)
Dim tanhArg As Double = Math.Tanh(arg)

' Evaluate tanh(X) = sinh(X) / cosh(X).
Console.WriteLine( _
vbCrLf & "                       Math.Tanh({0}) = {1:E16}" & _
vbCrLf & "      Math.Sinh({0}) / Math.Cosh({0}) = {2:E16}", _
arg, tanhArg, Math.Sinh(arg) / Math.Cosh(arg))

' Evaluate tanh(2 * X) = 2 * tanh(X) / (1 + tanh^2(X)).
Console.WriteLine( _
"                   2 * Math.Tanh({0}) /", _
arg, 2.0 * tanhArg)
Console.WriteLine( _
"             (1 + (Math.Tanh({0}))^2) = {1:E16}", _
arg, 2.0 * tanhArg /(1.0 + tanhArg * tanhArg))
Console.WriteLine( _
"                       Math.Tanh({0}) = {1:E16}", _
2.0 * arg, Math.Tanh((2.0 * arg)))
End Sub 'UseTanh

' Evaluate a hyperbolic identity that is a function of two arguments.
Sub UseTwoArgs(argX As Double, argY As Double)

' Evaluate tanh(X + Y) = (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
Console.WriteLine( _
vbCrLf & "    (Math.Tanh({0}) + Math.Tanh({1})) /" & _
vbCrLf & "(1 + Math.Tanh({0}) * Math.Tanh({1})) = {2:E16}", _
argX, argY, (Math.Tanh(argX) + Math.Tanh(argY)) / _
(1.0 + Math.Tanh(argX) * Math.Tanh(argY)))
Console.WriteLine( _
"                       Math.Tanh({0}) = {1:E16}", _
argX + argY, Math.Tanh(argX + argY))

End Sub 'UseTwoArgs
End Module 'DemoTanh

' This example of hyperbolic Math.Tanh( Double )
' generates the following output.
'
' Evaluate these hyperbolic identities with selected values for X:
'    tanh(X) = sinh(X) / cosh(X)
'    tanh(2 * X) = 2 * tanh(X) / (1 + tanh^2(X))
'
'                        Math.Tanh(0.1) = 9.9667994624955819E-002
'       Math.Sinh(0.1) / Math.Cosh(0.1) = 9.9667994624955819E-002
'                    2 * Math.Tanh(0.1) /
'              (1 + (Math.Tanh(0.1))^2) = 1.9737532022490401E-001
'                        Math.Tanh(0.2) = 1.9737532022490401E-001
'
'                        Math.Tanh(1.2) = 8.3365460701215521E-001
'       Math.Sinh(1.2) / Math.Cosh(1.2) = 8.3365460701215521E-001
'                    2 * Math.Tanh(1.2) /
'              (1 + (Math.Tanh(1.2))^2) = 9.8367485769368024E-001
'                        Math.Tanh(2.4) = 9.8367485769368024E-001
'
'                        Math.Tanh(4.9) = 9.9988910295055444E-001
'       Math.Sinh(4.9) / Math.Cosh(4.9) = 9.9988910295055433E-001
'                    2 * Math.Tanh(4.9) /
'              (1 + (Math.Tanh(4.9))^2) = 9.9999999385024030E-001
'                        Math.Tanh(9.8) = 9.9999999385024030E-001
'
' Evaluate [tanh(X + Y) == (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y))]
' with selected values for X and Y:
'
'     (Math.Tanh(0.1) + Math.Tanh(1.2)) /
' (1 + Math.Tanh(0.1) * Math.Tanh(1.2)) = 8.6172315931330645E-001
'                        Math.Tanh(1.3) = 8.6172315931330634E-001
'
'     (Math.Tanh(1.2) + Math.Tanh(4.9)) /
' (1 + Math.Tanh(1.2) * Math.Tanh(4.9)) = 9.9998993913939649E-001
'                        Math.Tanh(6.1) = 9.9998993913939649E-001

## Version Information

#### .NET Framework

Supported in: 4.6, 4.5, 4, 3.5, 3.0, 2.0, 1.1

#### .NET Framework Client Profile

Supported in: 4, 3.5 SP1

#### XNA Framework

Supported in: 3.0, 2.0, 1.0

#### Portable Class Library

Supported in: Portable Class Library
Supported in: Windows Phone 8.1
Supported in: Windows Phone Silverlight 8.1
Supported in: Windows Phone Silverlight 8