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Math.Sinh Method

Returns the hyperbolic sine of the specified angle.

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

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

returnValue = Math.Sinh(value)

Parameters

value
Type: System.Double

An angle, measured in radians.

Return Value

Type: System.Double
The hyperbolic sine of value. If value is equal to NegativeInfinity, PositiveInfinity, or NaN, this method returns a Double equal to value.

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

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

' Example for the hyperbolic Math.Sinh( Double ) and Math.Cosh( Double ) methods. 
Imports System
Imports Microsoft.VisualBasic

Module SinhCosh

    Sub Main()
        Console.WriteLine( _
            "This example of hyperbolic " & _
            "Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
            "generates the following output." & vbCrLf)
        Console.WriteLine( _
            "Evaluate these hyperbolic identities " & _
            "with selected values for X:")
        Console.WriteLine( _
            "   cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
            "   sinh(2 * X) = 2 * sinh(X) * cosh(X)")
        Console.WriteLine("   cosh(2 * X) = cosh^2(X) + sinh^2(X)")

        UseSinhCosh(0.1)
        UseSinhCosh(1.2)
        UseSinhCosh(4.9)

        Console.WriteLine( _
            vbCrLf & "Evaluate these hyperbolic " & _
            "identities with selected values for X and Y:")
        Console.WriteLine( _
            "   sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)")
        Console.WriteLine( _
            "   cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)")

        UseTwoArgs(0.1, 1.2)
        UseTwoArgs(1.2, 4.9)
    End Sub 'Main

    ' Evaluate hyperbolic identities with a given argument. 
    Sub UseSinhCosh(arg As Double)
        Dim sinhArg As Double = Math.Sinh(arg)
        Dim coshArg As Double = Math.Cosh(arg)

        ' Evaluate cosh^2(X) - sinh^2(X) = 1.
        Console.WriteLine( _
            vbCrLf & "                         Math.Sinh({0}) = {1:E16}" + _
            vbCrLf & "                         Math.Cosh({0}) = {2:E16}", _
            arg, Math.Sinh(arg), Math.Cosh(arg))
        Console.WriteLine( _
            "(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 = {1:E16}", _
            arg, coshArg * coshArg - sinhArg * sinhArg)

        ' Evaluate sinh(2 * X) = 2 * sinh(X) * cosh(X).
        Console.WriteLine( _
            "                         Math.Sinh({0}) = {1:E16}", _
            2.0 * arg, Math.Sinh((2.0 * arg)))
        Console.WriteLine( _
            "    2 * Math.Sinh({0}) * Math.Cosh({0}) = {1:E16}", _
            arg, 2.0 * sinhArg * coshArg)

        ' Evaluate cosh(2 * X) = cosh^2(X) + sinh^2(X).
        Console.WriteLine( _
            "                         Math.Cosh({0}) = {1:E16}", _
            2.0 * arg, Math.Cosh((2.0 * arg)))
        Console.WriteLine( _
            "(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 = {1:E16}", _
            arg, coshArg * coshArg + sinhArg * sinhArg)

    End Sub 'UseSinhCosh

    ' Evaluate hyperbolic identities that are functions of two arguments. 
    Sub UseTwoArgs(argX As Double, argY As Double)

        ' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
        Console.WriteLine( _
            vbCrLf & "        Math.Sinh({0}) * Math.Cosh({1}) +" + _
            vbCrLf & "        Math.Cosh({0}) * Math.Sinh({1}) = {2:E16}", _
            argX, argY, Math.Sinh(argX) * Math.Cosh(argY) + _
            Math.Cosh(argX) * Math.Sinh(argY))
        Console.WriteLine( _
            "                         Math.Sinh({0}) = {1:E16}", _
            argX + argY, Math.Sinh((argX + argY)))

        ' Evaluate cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
        Console.WriteLine( _
            "        Math.Cosh({0}) * Math.Cosh({1}) +" + _
            vbCrLf & "        Math.Sinh({0}) * Math.Sinh({1}) = {2:E16}", _
            argX, argY, Math.Cosh(argX) * Math.Cosh(argY) + _
            Math.Sinh(argX) * Math.Sinh(argY))
        Console.WriteLine( _
            "                         Math.Cosh({0}) = {1:E16}", _
            argX + argY, Math.Cosh((argX + argY)))

    End Sub 'UseTwoArgs
End Module 'SinhCosh

' This example of hyperbolic Math.Sinh( Double ) and Math.Cosh( Double ) 
' generates the following output. 
'  
' Evaluate these hyperbolic identities with selected values for X: 
'    cosh^2(X) - sinh^2(X) = 1 
'    sinh(2 * X) = 2 * sinh(X) * cosh(X) 
'    cosh(2 * X) = cosh^2(X) + sinh^2(X) 
'  
'                          Math.Sinh(0.1) = 1.0016675001984403E-001 
'                          Math.Cosh(0.1) = 1.0050041680558035E+000 
' (Math.Cosh(0.1))^2 - (Math.Sinh(0.1))^2 = 9.9999999999999989E-001 
'                          Math.Sinh(0.2) = 2.0133600254109399E-001 
'     2 * Math.Sinh(0.1) * Math.Cosh(0.1) = 2.0133600254109396E-001 
'                          Math.Cosh(0.2) = 1.0200667556190759E+000 
' (Math.Cosh(0.1))^2 + (Math.Sinh(0.1))^2 = 1.0200667556190757E+000 
'  
'                          Math.Sinh(1.2) = 1.5094613554121725E+000 
'                          Math.Cosh(1.2) = 1.8106555673243747E+000 
' (Math.Cosh(1.2))^2 - (Math.Sinh(1.2))^2 = 1.0000000000000000E+000 
'                          Math.Sinh(2.4) = 5.4662292136760939E+000 
'     2 * Math.Sinh(1.2) * Math.Cosh(1.2) = 5.4662292136760939E+000 
'                          Math.Cosh(2.4) = 5.5569471669655064E+000 
' (Math.Cosh(1.2))^2 + (Math.Sinh(1.2))^2 = 5.5569471669655064E+000 
'  
'                          Math.Sinh(4.9) = 6.7141166550932297E+001 
'                          Math.Cosh(4.9) = 6.7148613134003227E+001 
' (Math.Cosh(4.9))^2 - (Math.Sinh(4.9))^2 = 1.0000000000000000E+000 
'                          Math.Sinh(9.8) = 9.0168724361884615E+003 
'     2 * Math.Sinh(4.9) * Math.Cosh(4.9) = 9.0168724361884615E+003 
'                          Math.Cosh(9.8) = 9.0168724916400624E+003 
' (Math.Cosh(4.9))^2 + (Math.Sinh(4.9))^2 = 9.0168724916400606E+003 
'  
' Evaluate these hyperbolic identities with selected values for X and Y: 
'    sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y) 
'    cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y) 
'  
'         Math.Sinh(0.1) * Math.Cosh(1.2) + 
'         Math.Cosh(0.1) * Math.Sinh(1.2) = 1.6983824372926155E+000 
'                          Math.Sinh(1.3) = 1.6983824372926160E+000 
'         Math.Cosh(0.1) * Math.Cosh(1.2) + 
'         Math.Sinh(0.1) * Math.Sinh(1.2) = 1.9709142303266281E+000 
'                          Math.Cosh(1.3) = 1.9709142303266285E+000 
'  
'         Math.Sinh(1.2) * Math.Cosh(4.9) + 
'         Math.Cosh(1.2) * Math.Sinh(4.9) = 2.2292776360739879E+002 
'                          Math.Sinh(6.1) = 2.2292776360739885E+002 
'         Math.Cosh(1.2) * Math.Cosh(4.9) + 
'         Math.Sinh(1.2) * Math.Sinh(4.9) = 2.2293000647511826E+002 
'                          Math.Cosh(6.1) = 2.2293000647511832E+002

Windows 7, Windows Vista, Windows XP SP2, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP Starter Edition, Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows Server 2000 SP4, Windows Millennium Edition, Windows 98, Windows CE, Windows Mobile for Smartphone, Windows Mobile for Pocket PC, Xbox 360, Zune

The .NET Framework and .NET Compact Framework do not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

.NET Framework

Supported in: 3.5, 3.0, 2.0, 1.1, 1.0

.NET Compact Framework

Supported in: 3.5, 2.0, 1.0

XNA Framework

Supported in: 3.0, 2.0, 1.0
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