# Math.Sinh Method

Returns the hyperbolic sine of the specified angle.

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

## Syntax

``````'Declaration
<SecuritySafeCriticalAttribute> _
Public Shared Function Sinh ( _
value As Double _
) As Double
``````
``````[SecuritySafeCriticalAttribute]
public static double Sinh(
double value
)
``````

#### Return Value

Type: System.Double
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 Math.PI/180 to convert degrees to radians.

## Examples

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.

Module Example

Public Sub Demo(ByVal outputBlock As System.Windows.Controls.TextBlock)
outputBlock.Text &= _
"This example of hyperbolic " & _
"Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
"generates the following output." & vbCrLf & vbCrLf
outputBlock.Text &= _
"Evaluate these hyperbolic identities " & _
"with selected values for X:" & vbCrLf
outputBlock.Text &= _
"   cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
"   sinh(2 * X) = 2 * sinh(X) * cosh(X)" & vbCrLf
outputBlock.Text &= "   cosh(2 * X) = cosh^2(X) + sinh^2(X)" & vbCrLf

UseExample(outputBlock, 0.1)
UseExample(outputBlock, 1.2)
UseExample(outputBlock, 4.9)

outputBlock.Text &= _
vbCrLf & "Evaluate these hyperbolic " & _
"identities with selected values for X and Y:" & vbCrLf
outputBlock.Text &= _
"   sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)" & vbCrLf
outputBlock.Text &= _
"   cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)" & vbCrLf

UseTwoArgs(outputBlock, 0.1, 1.2)
UseTwoArgs(outputBlock, 1.2, 4.9)
End Sub 'Main

' Evaluate hyperbolic identities with a given argument.
Sub UseExample(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal arg As Double)
Dim sinhArg As Double = Math.Sinh(arg)
Dim coshArg As Double = Math.Cosh(arg)

' Evaluate cosh^2(X) - sinh^2(X) = 1.
outputBlock.Text &= String.Format( _
vbCrLf & "                         Math.Sinh({0}) = {1:E16}" + _
vbCrLf & "                         Math.Cosh({0}) = {2:E16}", _
arg, Math.Sinh(arg), Math.Cosh(arg)) & vbCrLf
outputBlock.Text &= String.Format( _
"(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 = {1:E16}", _
arg, coshArg * coshArg - sinhArg * sinhArg) & vbCrLf

' Evaluate sinh(2 * X) = 2 * sinh(X) * cosh(X).
outputBlock.Text &= String.Format( _
"                         Math.Sinh({0}) = {1:E16}", _
2.0 * arg, Math.Sinh((2.0 * arg))) & vbCrLf
outputBlock.Text &= String.Format( _
"    2 * Math.Sinh({0}) * Math.Cosh({0}) = {1:E16}", _
arg, 2.0 * sinhArg * coshArg) & vbCrLf

' Evaluate cosh(2 * X) = cosh^2(X) + sinh^2(X).
outputBlock.Text &= String.Format( _
"                         Math.Cosh({0}) = {1:E16}", _
2.0 * arg, Math.Cosh((2.0 * arg))) & vbCrLf
outputBlock.Text &= String.Format( _
"(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 = {1:E16}", _
arg, coshArg * coshArg + sinhArg * sinhArg) & vbCrLf

End Sub 'UseExample

' Evaluate hyperbolic identities that are functions of two arguments.
Sub UseTwoArgs(ByVal outputBlock As System.Windows.Controls.TextBlock, ByVal argX As Double, ByVal argY As Double)

' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
outputBlock.Text &= String.Format( _
vbCrLf & "        Math.Sinh({0}) * Math.Cosh({1}) +" + _
vbCrLf & "        Math.Cosh({0}) * Math.Sinh({1}) = {2:E16}", _
argX, argY, Math.Sinh(argX) * Math.Cosh(argY) + _
Math.Cosh(argX) * Math.Sinh(argY)) & vbCrLf
outputBlock.Text &= String.Format( _
"                         Math.Sinh({0}) = {1:E16}", _
argX + argY, Math.Sinh((argX + argY))) & vbCrLf

' Evaluate cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
outputBlock.Text &= String.Format( _
"        Math.Cosh({0}) * Math.Cosh({1}) +" + _
vbCrLf & "        Math.Sinh({0}) * Math.Sinh({1}) = {2:E16}", _
argX, argY, Math.Cosh(argX) * Math.Cosh(argY) + _
Math.Sinh(argX) * Math.Sinh(argY)) & vbCrLf
outputBlock.Text &= String.Format( _
"                         Math.Cosh({0}) = {1:E16}", _
argX + argY, Math.Cosh((argX + argY))) & vbCrLf

End Sub 'UseTwoArgs
End Module '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
``````
``````// Example for the hyperbolic Math.Sinh( double )
// and Math.Cosh( double ) methods.
using System;

class Example
{
public static void Demo(System.Windows.Controls.TextBlock outputBlock)
{
outputBlock.Text +=
"This example of hyperbolic Math.Sinh( double ) " +
"and Math.Cosh( double )\n" +
"generates the following output.\n" + "\n";
outputBlock.Text +=
"Evaluate these hyperbolic identities " +
"with selected values for X:" + "\n";
outputBlock.Text +=
"   cosh^2(X) - sinh^2(X) == 1\n" +
"   sinh(2 * X) == 2 * sinh(X) * cosh(X)" + "\n";
outputBlock.Text += "   cosh(2 * X) == cosh^2(X) + sinh^2(X)" + "\n";

UseExample(outputBlock, 0.1);
UseExample(outputBlock, 1.2);
UseExample(outputBlock, 4.9);

outputBlock.Text +=
"\nEvaluate these hyperbolic identities " +
"with selected values for X and Y:" + "\n";
outputBlock.Text +=
"   sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y)" + "\n";
outputBlock.Text +=
"   cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y)" + "\n";

UseTwoArgs(outputBlock, 0.1, 1.2);
UseTwoArgs(outputBlock, 1.2, 4.9);
}

// Evaluate hyperbolic identities with a given argument.
static void UseExample(System.Windows.Controls.TextBlock outputBlock, double arg)
{
double sinhArg = Math.Sinh(arg);
double coshArg = Math.Cosh(arg);

// Evaluate cosh^2(X) - sinh^2(X) == 1.
outputBlock.Text += String.Format(
"\n                         Math.Sinh({0}) == {1:E16}\n" +
"                         Math.Cosh({0}) == {2:E16}",
arg, Math.Sinh(arg), Math.Cosh(arg)) + "\n";
outputBlock.Text += String.Format(
"(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 == {1:E16}",
arg, coshArg * coshArg - sinhArg * sinhArg) + "\n";

// Evaluate sinh(2 * X) == 2 * sinh(X) * cosh(X).
outputBlock.Text += String.Format(
"                         Math.Sinh({0}) == {1:E16}",
2.0 * arg, Math.Sinh(2.0 * arg)) + "\n";
outputBlock.Text += String.Format(
"    2 * Math.Sinh({0}) * Math.Cosh({0}) == {1:E16}",
arg, 2.0 * sinhArg * coshArg) + "\n";

// Evaluate cosh(2 * X) == cosh^2(X) + sinh^2(X).
outputBlock.Text += String.Format(
"                         Math.Cosh({0}) == {1:E16}",
2.0 * arg, Math.Cosh(2.0 * arg)) + "\n";
outputBlock.Text += String.Format(
"(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 == {1:E16}",
arg, coshArg * coshArg + sinhArg * sinhArg) + "\n";
}

// Evaluate hyperbolic identities that are functions of two arguments.
static void UseTwoArgs(System.Windows.Controls.TextBlock outputBlock, double argX, double argY)
{
// Evaluate sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
outputBlock.Text += String.Format(
"\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)) + "\n";
outputBlock.Text += String.Format(
"                         Math.Sinh({0}) == {1:E16}",
argX + argY, Math.Sinh(argX + argY)) + "\n";

// Evaluate cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
outputBlock.Text += String.Format(
"        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)) + "\n";
outputBlock.Text += String.Format(
"                         Math.Cosh({0}) == {1:E16}",
argX + argY, Math.Cosh(argX + argY)) + "\n";
}
}

/*
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

#### Silverlight

Supported in: 5, 4, 3

#### Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

#### XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

## Platforms

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.