This documentation is archived and is not being maintained.

# Math.Sinh Method

.NET Framework 2.0

Returns the hyperbolic sine of the specified angle.

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

## Syntax

```public:
static double Sinh (
double value
)
```
```public static double Sinh (
double value
)
```
```public static function Sinh (
value : double
) : double
```

#### Parameters

value

An angle, measured in radians.

#### Return Value

The hyperbolic sine of value. If value is equal to NegativeInfinity, PositiveInfinity, or NaN, this method returns a Double equal to value.

## Remarks

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

## Example

The following example uses Sinh 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
*/

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

## Version Information

#### .NET Framework

Supported in: 2.0, 1.1, 1.0

#### .NET Compact Framework

Supported in: 2.0, 1.0

Math Class
Math Members
System Namespace
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