Math::Cosh Method

Returns the hyperbolic cosine of the specified angle.

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

public:
static double Cosh(
	double value
)

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.

// 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
*/

.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

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.

Was this page helpful?
(1500 characters remaining)
Thank you for your feedback
Show:
© 2014 Microsoft