Math.Tanh(Double) 方法
定义
返回指定角度的双曲正切值。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
参数
- value
- Double
以弧度计量的角度。An angle, measured in radians.
返回
value 的双曲正切值。The hyperbolic tangent of value. 如果 value 等于 NegativeInfinity,则此方法返回 -1。If value is equal to NegativeInfinity, this method returns -1. 如果值等于 PositiveInfinity,则此方法返回 1。If value is equal to PositiveInfinity, this method returns 1. 如果 value 等于 NaN,则此方法返回 NaN。If value is equal to NaN, this method returns NaN.
示例
下面的示例使用 Tanh 来计算选定值的某些双曲正切标识。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
注解
角度( value )必须为弧度。The angle, value, must be in radians. 乘以 Math.PI /180 将度转换为弧度。Multiply by Math.PI/180 to convert degrees to radians.
此方法调入基础 C 运行时,并且不同的操作系统或体系结构的确切结果或有效输入范围可能不同。This method calls into the underlying C runtime, and the exact result or valid input range may differ between different operating systems or architectures.