Math.Tanh Method
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Returns the hyperbolic tangent of the specified angle.
Namespace: System
Assembly: mscorlib (in mscorlib.dll)
Syntax
'Declaration
<SecuritySafeCriticalAttribute> _
Public Shared Function Tanh ( _
value As Double _
) As Double
[SecuritySafeCriticalAttribute]
public static double Tanh(
double value
)
Parameters
- value
Type: System.Double
An angle, measured in radians.
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.
Module Example
Public Sub Demo(ByVal outputBlock As System.Windows.Controls.TextBlock)
outputBlock.Text &= _
"This example of hyperbolic Math.Tanh( Double )" & _
vbCrLf & "generates the following output." & vbCrLf
outputBlock.Text &= _
vbCrLf & "Evaluate these hyperbolic " & _
"identities with selected values for X:" & vbCrLf
outputBlock.Text &= " tanh(X) = sinh(X) / cosh(X)" & vbCrLf
outputBlock.Text &= " tanh(2 * X) = 2 * tanh(X) / (1 + tanh^2(X))" & vbCrLf
UseTanh(outputBlock, 0.1)
UseTanh(outputBlock, 1.2)
UseTanh(outputBlock, 4.9)
outputBlock.Text &= _
vbCrLf & "Evaluate [tanh(X + Y) == (tanh(X) + " & _
"tanh(Y)) / (1 + tanh(X) * tanh(Y))]" & _
vbCrLf & "with selected values for X and 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 UseTanh(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal arg As Double)
Dim tanhArg As Double = Math.Tanh(arg)
' Evaluate tanh(X) = sinh(X) / cosh(X).
outputBlock.Text &= String.Format( _
vbCrLf & " Math.Tanh({0}) = {1:E16}" & _
vbCrLf & " Math.Sinh({0}) / Math.Cosh({0}) = {2:E16}", _
arg, tanhArg, Math.Sinh(arg) / Math.Cosh(arg)) & vbCrLf
' Evaluate tanh(2 * X) = 2 * tanh(X) / (1 + tanh^2(X)).
outputBlock.Text &= String.Format( _
" 2 * Math.Tanh({0}) /", _
arg, 2.0 * tanhArg) & vbCrLf
outputBlock.Text &= String.Format( _
" (1 + (Math.Tanh({0}))^2) = {1:E16}", _
arg, 2.0 * tanhArg / (1.0 + tanhArg * tanhArg)) & vbCrLf
outputBlock.Text &= String.Format( _
" Math.Tanh({0}) = {1:E16}", _
2.0 * arg, Math.Tanh((2.0 * arg))) & vbCrLf
End Sub 'UseTanh
' Evaluate a hyperbolic identity that is a function of two arguments.
Sub UseTwoArgs(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal argX As Double, ByVal argY As Double)
' Evaluate tanh(X + Y) = (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
outputBlock.Text &= String.Format( _
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))) & vbCrLf
outputBlock.Text &= String.Format( _
" Math.Tanh({0}) = {1:E16}", _
argX + argY, Math.Tanh(argX + argY)) & vbCrLf
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
// Example for the hyperbolic Math.Tanh( double ) method.
using System;
class Example
{
public static void Demo(System.Windows.Controls.TextBlock outputBlock)
{
outputBlock.Text +=
"This example of hyperbolic Math.Tanh( double )\n" +
"generates the following output." + "\n";
outputBlock.Text +=
"\nEvaluate these hyperbolic identities " +
"with selected values for X:" + "\n";
outputBlock.Text += " tanh(X) == sinh(X) / cosh(X)" + "\n";
outputBlock.Text +=
" tanh(2 * X) == 2 * tanh(X) / (1 + tanh^2(X))" + "\n";
UseTanh(outputBlock, 0.1);
UseTanh(outputBlock, 1.2);
UseTanh(outputBlock, 4.9);
outputBlock.Text +=
"\nEvaluate [tanh(X + Y) == (tanh(X) + tanh(Y)) " +
"/ (1 + tanh(X) * tanh(Y))]" +
"\nwith selected values for X and Y:" + "\n";
UseTwoArgs(outputBlock, 0.1, 1.2);
UseTwoArgs(outputBlock, 1.2, 4.9);
}
// Evaluate hyperbolic identities with a given argument.
static void UseTanh(System.Windows.Controls.TextBlock outputBlock, double arg)
{
double tanhArg = Math.Tanh(arg);
// Evaluate tanh(X) == sinh(X) / cosh(X).
outputBlock.Text += String.Format(
"\n Math.Tanh({0}) == {1:E16}\n" +
" Math.Sinh({0}) / Math.Cosh({0}) == {2:E16}",
arg, tanhArg, (Math.Sinh(arg) / Math.Cosh(arg))) + "\n";
// Evaluate tanh(2 * X) == 2 * tanh(X) / (1 + tanh^2(X)).
outputBlock.Text += String.Format(
" 2 * Math.Tanh({0}) /",
arg, 2.0 * tanhArg) + "\n";
outputBlock.Text += String.Format(
" (1 + (Math.Tanh({0}))^2) == {1:E16}",
arg, 2.0 * tanhArg / (1.0 + tanhArg * tanhArg)) + "\n";
outputBlock.Text += String.Format(
" Math.Tanh({0}) == {1:E16}",
2.0 * arg, Math.Tanh(2.0 * arg)) + "\n";
}
// Evaluate a hyperbolic identity that is a function of two arguments.
static void UseTwoArgs(System.Windows.Controls.TextBlock outputBlock, double argX, double argY)
{
// Evaluate tanh(X + Y) == (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
outputBlock.Text += String.Format(
"\n (Math.Tanh({0}) + Math.Tanh({1})) /\n" +
"(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))) + "\n";
outputBlock.Text += String.Format(
" Math.Tanh({0}) == {1:E16}",
argX + argY, Math.Tanh(argX + argY)) + "\n";
}
}
/*
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
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.