Microsoft Developer Network
 Cosh Method
.NET Framework Class Library
Math..::.Cosh Method

Returns the hyperbolic cosine of the specified angle.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)
Visual Basic (Declaration)
Public Shared Function Cosh ( _
    value As Double _
) As Double
Visual Basic (Usage)
Dim value As Double
Dim returnValue As Double

returnValue = Math.Cosh(value)
C#
public static double Cosh(
    double value
)
Visual C++
public:
static double Cosh(
    double value
)
JScript
public static function Cosh(
    value : double
) : double

Parameters

value
Type: System..::.Double
An angle, measured in radians.

Return Value

Type: System..::.Double
The hyperbolic cosine of value. If value is equal to NegativeInfinity or PositiveInfinity, PositiveInfinity is returned. If value is equal to NaN, NaN is returned.

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

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

Visual Basic
' 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
C#
// Example for the hyperbolic Math.Sinh( double ) 
// and Math.Cosh( double ) methods.
using System;

class SinhCosh 
{
    public static void Main() 
    {
        Console.WriteLine( 
            "This example of hyperbolic Math.Sinh( double ) " +
            "and Math.Cosh( double )\n" +
            "generates the following output.\n" );
        Console.WriteLine( 
            "Evaluate these hyperbolic identities " +
            "with selected values for X:" );
        Console.WriteLine( 
            "   cosh^2(X) - sinh^2(X) == 1\n" +
            "   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( 
            "\nEvaluate 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);
    }

    // Evaluate hyperbolic identities with a given argument.
    static void UseSinhCosh(double arg)
    {
        double sinhArg = Math.Sinh(arg);
        double coshArg = Math.Cosh(arg);

        // Evaluate cosh^2(X) - sinh^2(X) == 1.
        Console.WriteLine( 
            "\n                         Math.Sinh({0}) == {1:E16}\n" +
            "                         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 );
    }

    // Evaluate hyperbolic identities that are functions of two arguments.
    static void UseTwoArgs(double argX, double argY)
    {
        // Evaluate sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
        Console.WriteLine( 
            "\n        Math.Sinh({0}) * Math.Cosh({1}) +\n" + 
            "        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}) +\n" + 
            "        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));
    }
}

/*
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
*/
Visual C++
// Example for the hyperbolic Math.Sinh( double ) 
// and Math.Cosh( double ) methods.
using namespace System;

// Evaluate hyperbolic identities with a given argument.
void UseSinhCosh( double arg )
{
   double sinhArg = Math::Sinh( arg );
   double coshArg = Math::Cosh( arg );

   // Evaluate cosh^2(X) - sinh^2(X) == 1.
   Console::WriteLine( "\n                          Math::Sinh({0}) == {1:E16}\n"
   "                          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 );
}


// Evaluate hyperbolic identities that are functions of two arguments.
void UseTwoArgs( double argX, double argY )
{

   // Evaluate sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
   Console::WriteLine( "\n        Math::Sinh({0}) * Math::Cosh({1}) +\n"
   "        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}) +\n"
   "        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 ) );
}

int main()
{
   Console::WriteLine( "This example of hyperbolic "
   "Math::Sinh( double ) and Math::Cosh( double )\n"
   "generates the following output.\n" );
   Console::WriteLine( "Evaluate these hyperbolic identities "
   "with selected values for X:" );
   Console::WriteLine( "   cosh^2(X) - sinh^2(X) == 1\n"
   "   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( "\nEvaluate 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 );
}

/*
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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