Math.Cosh Method

Silverlight

Returns the hyperbolic cosine of the specified angle.

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

Syntax

```'Declaration
<SecuritySafeCriticalAttribute> _
Public Shared Function Cosh ( _
value As Double _
) As Double
```

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.

Remarks

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

Examples

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.

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

```

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.