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# Math.Tanh Method

.NET Framework 3.0
Returns the hyperbolic tangent of the specified angle.

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

## Syntax

```public static double Tanh (
double value
)
```
```public static double Tanh (
double value
)
```
```public static function Tanh (
value : double
) : double
```
```Not applicable.
```

value

#### Return Value

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.

## Example

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

```// Example for the hyperbolic Math.Tanh( double ) method.
using System;

class DemoTanh
{
public static void Main()
{
Console.WriteLine(
"This example of hyperbolic Math.Tanh( double )\n" +
"generates the following output." );
Console.WriteLine(
"\nEvaluate 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(
"\nEvaluate [tanh(X + Y) == (tanh(X) + tanh(Y)) " +
"/ (1 + tanh(X) * tanh(Y))]" +
"\nwith selected values for X and Y:" );

UseTwoArgs(0.1, 1.2);
UseTwoArgs(1.2, 4.9);
}

// Evaluate hyperbolic identities with a given argument.
static void UseTanh(double arg)
{
double tanhArg = Math.Tanh(arg);

// Evaluate tanh(X) == sinh(X) / cosh(X).
Console.WriteLine(
"\n                       Math.Tanh({0}) == {1:E16}\n" +
"      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) );
}

// Evaluate a hyperbolic identity that is a function of two arguments.
static void UseTwoArgs(double argX, double argY)
{
// Evaluate tanh(X + Y) == (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
Console.WriteLine(
"\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)) );
Console.WriteLine(
"                       Math.Tanh({0}) == {1:E16}",
argX + argY, Math.Tanh(argX + argY));
}
}

/*
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.
import System.*;

class DemoTanh
{
public static void main(String[] args)
{
Console.WriteLine(("This example of hyperbolic Math.Tanh( double )\n"
+ "generates the following output."));
Console.WriteLine(
("\nEvaluate 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(
("\nEvaluate [tanh(X + Y) == (tanh(X) + tanh(Y)) "
+ "/ (1 + tanh(X) * tanh(Y))]"
+ "\nwith selected values for X and Y:"));
UseTwoArgs(0.1, 1.2);
UseTwoArgs(1.2, 4.9);
} //main

// Evaluate hyperbolic identities with a given argument.
static void UseTanh(double arg)
{
double tanhArg = System.Math.Tanh(arg);

// Evaluate tanh(X) == sinh(X) / cosh(X).
Console.WriteLine(
"\n                       Math.Tanh({0}) == {1}\n"
+ "      Math.Sinh({0}) / Math.Cosh({0}) == {2}",
System.Convert.ToString(arg),
((System.Double)(tanhArg)).ToString("E16"),
((System.Double)(System.Math.Sinh(arg) /
System.Math.Cosh(arg))).ToString("E16"));

// Evaluate tanh(2 * X) == 2 * tanh(X) / (1 + tanh^2(X)).
Console.WriteLine(
"                   2 * Math.Tanh({0}) /",
System.Convert.ToString(arg),
((System.Double)(2.0 * tanhArg)).ToString("E16"));
Console.WriteLine(
"             (1 + (Math.Tanh({0}))^2) == {1}",
System.Convert.ToString(arg),((System.Double)( 2.0 * tanhArg /
(1.0 + tanhArg * tanhArg))).ToString("E16"));
Console.WriteLine(
"                       Math.Tanh({0}) == {1}",
System.Convert.ToString(2.0 * arg),
((System.Double)( System.Math.Tanh((2.0 * arg)))).ToString("E16"));
} //UseTanh

// Evaluate a hyperbolic identity that is a function of two arguments.
static void UseTwoArgs(double argX, double argY)
{
// Evaluate tanh(X + Y) ==
// (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
Console.WriteLine(
"\n    (Math.Tanh({0}) + Math.Tanh({1})) /\n"
+ "(1 + Math.Tanh({0}) * Math.Tanh({1})) == {2}",
System.Convert.ToString(argX),
System.Convert.ToString(argY),
((System.Double) ((System.Math.Tanh(argX)
+ System.Math.Tanh(argY)) / (1.0 + System.Math.Tanh(argX)
* System.Math.Tanh(argY)))).ToString("E16"));
Console.WriteLine(
"                       Math.Tanh({0}) == {1}",
System.Convert.ToString (argX + argY),((System.Double)(
System.Math.Tanh((argX + argY)))).ToString("E16"));
} //UseTwoArgs
} //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
*/

```

## Platforms

Windows 98, Windows Server 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile for Pocket PC, Windows Mobile for Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

The Microsoft .NET Framework 3.0 is supported on Windows Vista, Microsoft Windows XP SP2, and Windows Server 2003 SP1.

## Version Information

#### .NET Framework

Supported in: 3.0, 2.0, 1.1, 1.0

#### .NET Compact Framework

Supported in: 2.0, 1.0

#### XNA Framework

Supported in: 1.0

Math Class
Math Members
System Namespace