Math.Tanh(Double) Metoda

Reference

Definice

Obor názvů:: System

Sestavení:: System.Runtime.Extensions.dll

Sestavení:: System.Runtime.dll

Sestavení:: mscorlib.dll

Sestavení:: netstandard.dll

Zdroj:: Math.cs

Zdroj:: Math.cs

Zdroj:: Math.cs

Důležité

Některé informace platí pro předběžně vydaný produkt, který se může zásadně změnit, než ho výrobce nebo autor vydá. Microsoft neposkytuje žádné záruky, výslovné ani předpokládané, týkající se zde uváděných informací.

Vrátí hyperbolický tangens zadaného úhlu.

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

Parametry

value: Double

Úhel měřený v radiánech.

Návraty

Double

Hyperbolický tangens funkce value. Pokud value se rovná hodnotě NegativeInfinity, vrátí tato metoda hodnotu -1. Pokud je hodnota rovna PositiveInfinity, vrátí tato metoda 1. Pokud value je hodnota rovna hodnotě NaN, vrátí NaNtato metoda hodnotu .

Příklady

Následující příklad používá Tanh k vyhodnocení určitých hyperbolických tangens identit pro vybrané hodnoty.

// 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

Poznámky

Úhel valuemusí být v radiánech. Vynásobením Math.PI/180 převedete stupně na radiány.

Tato metoda volá základní modul runtime jazyka C a přesný výsledek nebo platný vstupní rozsah se může v různých operačních systémech nebo architekturách lišit.

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