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# Math.Cosh Method

.NET Framework 3.5

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

#### 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 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
*/
```

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