# Math::Cosh Method

.NET Framework 4.5

Returns the hyperbolic cosine of the specified angle.

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

## Syntax

public:
static double Cosh(
double value
)

#### Parameters

value
Type: System::Double

#### 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.

## Remarks

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

## Examples

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

// 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
*/

## Version Information

#### .NET Framework

Supported in: 4.5, 4, 3.5, 3.0, 2.0, 1.1, 1.0

#### .NET Framework Client Profile

Supported in: 4, 3.5 SP1

#### Portable Class Library

Supported in: Portable Class Library

#### .NET for Windows Store apps

Supported in: Windows 8

#### .NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone Silverlight 8.1, Windows Phone Silverlight 8

## Platforms

Windows Phone 8.1, Windows Phone 8, Windows 8.1, Windows Server 2012 R2, Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)

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