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Math.Sinh Method

Returns the hyperbolic sine of the specified angle.

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

public static double Sinh(
	double value
)

Parameters

value
Type: System.Double

An angle, measured in radians.

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.

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

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. 
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
*/

.NET Framework

Supported in: 4.5.2, 4.5.1, 4.5, 4, 3.5, 3.0, 2.0, 1.1, 1.0

.NET Framework Client Profile

Supported in: 4, 3.5 SP1

Portable Class Library

Supported in: Portable Class Library

.NET for Windows Store apps

Supported in: Windows 8

.NET for Windows Phone apps

Supported in: Windows Phone 8.1, Windows Phone 8, Silverlight 8.1

Windows Phone 8.1, Windows Phone 8, Windows 8.1, Windows Server 2012 R2, Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

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