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Tradução
Inglês

Math.Sinh Método

Retorna o seno hiperbólico do ângulo especificado.

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

public static double Sinh(
	double value
)

Parâmetros

value
Tipo: System.Double
Um ângulo, medida em radianos.

Valor de retorno

Tipo: 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
*/


// 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
*/


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