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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
)
public static double Sinh (
	double value
)
public static function Sinh (
	value : double
) : double

Parameters

value

An angle, measured in radians.

Return Value

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 π/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
*/

// Example for the hyperbolic Math.Sinh( double ) 
// and Math.Cosh( double ) methods.
import System.*;

class SinhCosh
{
    public static void main(String[] args)
    {
        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);
    } //main
   
    // Evaluate hyperbolic identities with a given argument.
    static void UseSinhCosh(double arg)
    {
        double sinhArg = System.Math.Sinh(arg);
        double coshArg = System.Math.Cosh(arg);
        // Evaluate cosh^2(X) - sinh^2(X) == 1.
        Console.WriteLine("\n                         Math.Sinh({0}) == {1}\n"
            + "                         Math.Cosh({0}) == {2}",
            System.Convert.ToString(arg), 
            ((System.Double)(System.Math.Sinh(arg))).ToString("E16"),             
            ((System.Double)(System.Math.Cosh(arg))).ToString("E16"));
        Console.WriteLine("(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 == {1}", 
            System.Convert.ToString(arg),((System.Double)(             
            coshArg * coshArg - sinhArg * sinhArg)).ToString("E16"));
        // Evaluate sinh(2 * X) == 2 * sinh(X) * cosh(X).
        Console.WriteLine("                         Math.Sinh({0}) == {1}", 
            System.Convert.ToString(2.0 * arg), 
            ((System.Double)(System.Math.Sinh((2.0 * arg)))).ToString("E16"));
        Console.WriteLine("    2 * Math.Sinh({0}) * Math.Cosh({0}) == {1}", 
            System.Convert.ToString(arg),
            ((System.Double)( 2.0 * sinhArg * coshArg)).ToString("E16"));
        // Evaluate cosh(2 * X) == cosh^2(X) + sinh^2(X).
        Console.WriteLine("                         Math.Cosh({0}) == {1}",
            System.Convert.ToString(2.0 * arg),((System.Double)(            
            System.Math.Cosh((2.0 * arg)))).ToString("E16"));
        Console.WriteLine("(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 == {1}",
            System.Convert.ToString(arg),((System.Double)(            
            coshArg * coshArg + sinhArg * sinhArg)).ToString("E16"));
    } //UseSinhCosh
      
    // 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}",
            System.Convert.ToString(argX), System.Convert.ToString(argY),
            ((System.Double)(System.Math.Sinh(argX)*System.Math.Cosh(argY)
            + System.Math.Cosh(argX)*
            System.Math.Sinh(argY))).ToString("E16"));
        Console.WriteLine("                         Math.Sinh({0}) == {1}", 
            System.Convert.ToString(argX + argY),((System.Double)(            
            System.Math.Sinh((argX + argY)))).ToString("E16"));

        // 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}", 
            System.Convert.ToString(argX), System.Convert.ToString(argY),
            ((System.Double)(System.Math.Cosh(argX)*System.Math.Cosh(argY)
            +    System.Math.Sinh(argX)
            * System.Math.Sinh(argY))).ToString("E16"));
        Console.WriteLine("                         Math.Cosh({0}) == {1}",
            System.Convert.ToString(argX + argY),((System.Double)(            
            System.Math.Cosh((argX + argY)))).ToString("E16") );
    } //UseTwoArgs
} //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
*/

Windows 98, Windows 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile for Pocket PC, Windows Mobile for Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

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

.NET Framework

Supported in: 2.0, 1.1, 1.0

.NET Compact Framework

Supported in: 2.0, 1.0

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