Cosh Method

Math.Cosh Method (Double)

 

Returns the hyperbolic cosine of the specified angle.

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

public static double Cosh(
	double value
)

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.
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
*/

Universal Windows Platform
Available since 4.5
.NET Framework
Available since 1.1
Portable Class Library
Supported in: portable .NET platforms
Silverlight
Available since 2.0
Windows Phone Silverlight
Available since 7.0
Windows Phone
Available since 8.1
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