Math.Cosh Method

Returns the hyperbolic cosine of the specified angle.

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

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

Parameters

value
Type: System.Double
An angle, measured in radians.

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.

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


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

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

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