Math.Tanh(Double) Method

Reference

Definition

Namespace:: System

Assembly:: System.Runtime.Extensions.dll

Assembly:: System.Runtime.dll

Assembly:: mscorlib.dll

Assembly:: netstandard.dll

Source:: Math.cs

Source:: Math.cs

Source:: Math.cs

Important

Some information relates to prerelease product that may be substantially modified before it’s released. Microsoft makes no warranties, express or implied, with respect to the information provided here.

Returns the hyperbolic tangent of the specified angle.

public:
 static double Tanh(double value);

public static double Tanh (double value);

static member Tanh : double -> double

Public Shared Function Tanh (value As Double) As Double

Parameters

value: Double

An angle, measured in radians.

Returns

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.

Examples

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

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

// Evaluate hyperbolic identities with a given argument.
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.
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 ) );
}

int 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 );
}

/*
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 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.
// In F#, the tanh function may be used instead 
open System

// Evaluate hyperbolic identities with a given argument.
let useTanh arg =
    let tanhArg = Math.Tanh arg

    // Evaluate tanh(X) = sinh(X) / cosh(X).
    printfn $"""
                       Math.Tanh({arg}) = {tanhArg:E16}
      Math.Sinh({arg}) / Math.Cosh({arg}) = {Math.Sinh arg / Math.Cosh arg:E16}"""

    // Evaluate tanh(2 * X) = 2 * tanh(X) / (1 + tanh^2(X)).
    printfn $"                   2 * Math.Tanh({arg}) / {2. * tanhArg}"
    printfn $"             (1 + (Math.Tanh({arg}))^2) = {2. * tanhArg / (1. + tanhArg * tanhArg):E16}"
    printfn $"                       Math.Tanh({2. * arg}) = {Math.Tanh(2. * arg):E16}"

// Evaluate a hyperbolic identity that is a function of two arguments.
let useTwoArgs argX argY =
    // Evaluate tanh(X + Y) = (tanh(X) + tanh(Y)) / (1 + tanh(X) * tanh(Y)).
    printfn $"\n    (Math.Tanh({argX}) + Math.Tanh({argY})) /\n(1 + Math.Tanh({argX}) * Math.Tanh({argY})) = {(Math.Tanh argX + Math.Tanh argY) / (1. + Math.Tanh argX * Math.Tanh argY):E16}"
    printfn $"                       Math.Tanh({argX + argY}) = {Math.Tanh(argX + argY):E16}"

printfn "This example of hyperbolic Math.Tanh( double )\ngenerates the following output."
printfn "\nEvaluate these hyperbolic identities with selected values for X:"
printfn "   tanh(X) = sinh(X) / cosh(X)"
printfn "   tanh(2 * X) = 2 * tanh(X) / (1 + tanh^2(X))"

useTanh 0.1
useTanh 1.2
useTanh 4.9

printfn "\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


// 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.
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
       
    ' 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
       
    ' 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
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

Remarks

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

This method calls into the underlying C runtime, and the exact result or valid input range may differ between different operating systems or architectures.

Applies to

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