This documentation is archived and is not being maintained.

# Math.Cosh Method

.NET Framework 3.0
Returns the hyperbolic cosine of the specified angle.

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

## Syntax

```public static double Cosh (
double value
)
```
```public static double Cosh (
double value
)
```
```public static function Cosh (
value : double
) : double
```
```Not applicable.
```

value

#### Return Value

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.

## Example

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
*/

```
```// Example for the hyperbolic Math.Sinh( double )
// and Math.Cosh( double ) methods.
import System.*;

class SinhCosh
{
public static void main(String[] args)
{
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);
} //main

// Evaluate hyperbolic identities with a given argument.
static void UseSinhCosh(double arg)
{
double sinhArg = System.Math.Sinh(arg);
double coshArg = System.Math.Cosh(arg);
// Evaluate cosh^2(X) - sinh^2(X) == 1.
Console.WriteLine("\n                         Math.Sinh({0}) == {1}\n"
+ "                         Math.Cosh({0}) == {2}",
System.Convert.ToString(arg),
((System.Double)(System.Math.Sinh(arg))).ToString("E16"),
((System.Double)(System.Math.Cosh(arg))).ToString("E16"));
Console.WriteLine("(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 == {1}",
System.Convert.ToString(arg),((System.Double)(
coshArg * coshArg - sinhArg * sinhArg)).ToString("E16"));
// Evaluate sinh(2 * X) == 2 * sinh(X) * cosh(X).
Console.WriteLine("                         Math.Sinh({0}) == {1}",
System.Convert.ToString(2.0 * arg),
((System.Double)(System.Math.Sinh((2.0 * arg)))).ToString("E16"));
Console.WriteLine("    2 * Math.Sinh({0}) * Math.Cosh({0}) == {1}",
System.Convert.ToString(arg),
((System.Double)( 2.0 * sinhArg * coshArg)).ToString("E16"));
// Evaluate cosh(2 * X) == cosh^2(X) + sinh^2(X).
Console.WriteLine("                         Math.Cosh({0}) == {1}",
System.Convert.ToString(2.0 * arg),((System.Double)(
System.Math.Cosh((2.0 * arg)))).ToString("E16"));
Console.WriteLine("(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 == {1}",
System.Convert.ToString(arg),((System.Double)(
coshArg * coshArg + sinhArg * sinhArg)).ToString("E16"));
} //UseSinhCosh

// 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}",
System.Convert.ToString(argX), System.Convert.ToString(argY),
((System.Double)(System.Math.Sinh(argX)*System.Math.Cosh(argY)
+ System.Math.Cosh(argX)*
System.Math.Sinh(argY))).ToString("E16"));
Console.WriteLine("                         Math.Sinh({0}) == {1}",
System.Convert.ToString(argX + argY),((System.Double)(
System.Math.Sinh((argX + argY)))).ToString("E16"));

// 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}",
System.Convert.ToString(argX), System.Convert.ToString(argY),
((System.Double)(System.Math.Cosh(argX)*System.Math.Cosh(argY)
+    System.Math.Sinh(argX)
* System.Math.Sinh(argY))).ToString("E16"));
Console.WriteLine("                         Math.Cosh({0}) == {1}",
System.Convert.ToString(argX + argY),((System.Double)(
System.Math.Cosh((argX + argY)))).ToString("E16") );
} //UseTwoArgs
} //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
*/

```

## Platforms

Windows 98, Windows Server 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile for Pocket PC, Windows Mobile for Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

The Microsoft .NET Framework 3.0 is supported on Windows Vista, Microsoft Windows XP SP2, and Windows Server 2003 SP1.

## Version Information

#### .NET Framework

Supported in: 3.0, 2.0, 1.1, 1.0

#### .NET Compact Framework

Supported in: 2.0, 1.0

#### XNA Framework

Supported in: 1.0