# Math.Tanh(Double) Método

## Definição

Retorna a tangente hiperbólica do ângulo especificado.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``

value
Double

#### Retornos

A tangente hiperbólica de `value`.The hyperbolic tangent of `value`. Se `value` for igual a NegativeInfinity, esse método retornará -1.If `value` is equal to NegativeInfinity, this method returns -1. Se o valor for igual a PositiveInfinity, esse método retornará 1.If value is equal to PositiveInfinity, this method returns 1. Se `value` for igual a NaN, esse método retornará NaN.If `value` is equal to NaN, this method returns NaN.

## Exemplos

O exemplo a seguir Tanh usa para avaliar determinadas identidades da tangente hiperbólica para os valores selecionados.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.
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
``````

## Comentários

O ângulo, `value`, deve estar em radianos.The angle, `value`, must be in radians. Multiplique por Math.PI/180 para converter graus em radianos.Multiply by Math.PI/180 to convert degrees to radians.