Math.Tanh-Methode

Gibt den Hyperbeltangens des angegebenen Winkels zurück.

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

Syntax

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

returnValue = Math.Tanh(value)

public static double Tanh (
    double value
)

public:
static double Tanh (
    double value
)

public static double Tanh (
    double value
)

public static function Tanh (
    value : double
) : double

Parameter

• value
  Ein im Bogenmaß angegebener Winkel.

Rückgabewert

Der Hyperbeltangens von value. Wenn value gleich NegativeInfinity ist, gibt diese Methode -1 zurück. Wenn value gleich PositiveInfinity ist, gibt diese Methode 1 zurück. Wenn value gleich NaN ist, gibt diese Methode NaN zurück.

Hinweise

Der Winkel value muss im Bogenmaß angegeben werden. Multiplizieren Sie den Wert zur Konvertierung von Grad in Bogenmaß mit π/180.

Beispiel

Im folgenden Beispiel werden mit Tanh bestimmte Hyperbeltangensidentitäten für ausgewählte Werte ausgewertet.

' 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

// 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.
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.
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
*/

Plattformen

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

.NET Framework unterstützt nicht alle Versionen sämtlicher Plattformen. Eine Liste der unterstützten Versionen finden Sie unter Systemanforderungen.

Versionsinformationen

.NET Framework

Unterstützt in: 2.0, 1.1, 1.0

.NET Compact Framework

Unterstützt in: 2.0, 1.0

Siehe auch

Referenz

Math-Klasse
Math-Member
System-Namespace