Math.Cosh(Double) Method

Definition

Returns the hyperbolic cosine of the specified angle.

public static double Cosh (double value);
Parameters
value
Double

An angle, measured in radians.

Returns

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.

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.
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.
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.
Imports System
Imports Microsoft.VisualBasic

Module SinhCosh
   
    Sub Main()
        Console.WriteLine( _
            "This example of hyperbolic " & _
            "Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
            "generates the following output." & vbCrLf)
        Console.WriteLine( _
            "Evaluate these hyperbolic identities " & _
            "with selected values for X:")
        Console.WriteLine( _
            "   cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
            "   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( _
            vbCrLf & "Evaluate 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)
    End Sub 'Main
      
    ' Evaluate hyperbolic identities with a given argument.
    Sub UseSinhCosh(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.
        Console.WriteLine( _
            vbCrLf & "                         Math.Sinh({0}) = {1:E16}" + _
            vbCrLf & "                         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)

    End Sub 'UseSinhCosh
       
    ' Evaluate hyperbolic identities that are functions of two arguments.
    Sub UseTwoArgs(argX As Double, argY As Double)

        ' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
        Console.WriteLine( _
            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))
        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}) +" + _
            vbCrLf & "        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)))

    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

Remarks

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

Applies to