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Math.Sinh Method

Returns the hyperbolic sine of the specified angle.

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

[SecuritySafeCriticalAttribute]
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 Example
{
   public static void Demo(System.Windows.Controls.TextBlock outputBlock)
   {
      outputBlock.Text +=
          "This example of hyperbolic Math.Sinh( double ) " +
          "and Math.Cosh( double )\n" +
          "generates the following output.\n" + "\n";
      outputBlock.Text +=
          "Evaluate these hyperbolic identities " +
          "with selected values for X:" + "\n";
      outputBlock.Text +=
          "   cosh^2(X) - sinh^2(X) == 1\n" +
          "   sinh(2 * X) == 2 * sinh(X) * cosh(X)" + "\n";
      outputBlock.Text += "   cosh(2 * X) == cosh^2(X) + sinh^2(X)" + "\n";

      UseExample(outputBlock, 0.1);
      UseExample(outputBlock, 1.2);
      UseExample(outputBlock, 4.9);

      outputBlock.Text +=
          "\nEvaluate these hyperbolic identities " +
          "with selected values for X and Y:" + "\n";
      outputBlock.Text +=
          "   sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y)" + "\n";
      outputBlock.Text +=
          "   cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y)" + "\n";

      UseTwoArgs(outputBlock, 0.1, 1.2);
      UseTwoArgs(outputBlock, 1.2, 4.9);
   }

   // Evaluate hyperbolic identities with a given argument.
   static void UseExample(System.Windows.Controls.TextBlock outputBlock, double arg)
   {
      double sinhArg = Math.Sinh(arg);
      double coshArg = Math.Cosh(arg);

      // Evaluate cosh^2(X) - sinh^2(X) == 1.
      outputBlock.Text += String.Format(
          "\n                         Math.Sinh({0}) == {1:E16}\n" +
          "                         Math.Cosh({0}) == {2:E16}",
          arg, Math.Sinh(arg), Math.Cosh(arg)) + "\n";
      outputBlock.Text += String.Format(
          "(Math.Cosh({0}))^2 - (Math.Sinh({0}))^2 == {1:E16}",
          arg, coshArg * coshArg - sinhArg * sinhArg) + "\n";

      // Evaluate sinh(2 * X) == 2 * sinh(X) * cosh(X).
      outputBlock.Text += String.Format(
          "                         Math.Sinh({0}) == {1:E16}",
          2.0 * arg, Math.Sinh(2.0 * arg)) + "\n";
      outputBlock.Text += String.Format(
          "    2 * Math.Sinh({0}) * Math.Cosh({0}) == {1:E16}",
          arg, 2.0 * sinhArg * coshArg) + "\n";

      // Evaluate cosh(2 * X) == cosh^2(X) + sinh^2(X).
      outputBlock.Text += String.Format(
          "                         Math.Cosh({0}) == {1:E16}",
          2.0 * arg, Math.Cosh(2.0 * arg)) + "\n";
      outputBlock.Text += String.Format(
          "(Math.Cosh({0}))^2 + (Math.Sinh({0}))^2 == {1:E16}",
          arg, coshArg * coshArg + sinhArg * sinhArg) + "\n";
   }

   // Evaluate hyperbolic identities that are functions of two arguments.
   static void UseTwoArgs(System.Windows.Controls.TextBlock outputBlock, double argX, double argY)
   {
      // Evaluate sinh(X + Y) == sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
      outputBlock.Text += String.Format(
          "\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)) + "\n";
      outputBlock.Text += String.Format(
          "                         Math.Sinh({0}) == {1:E16}",
          argX + argY, Math.Sinh(argX + argY)) + "\n";

      // Evaluate cosh(X + Y) == cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
      outputBlock.Text += String.Format(
          "        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)) + "\n";
      outputBlock.Text += String.Format(
          "                         Math.Cosh({0}) == {1:E16}",
          argX + argY, Math.Cosh(argX + argY)) + "\n";
   }
}

/*
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
*/


Silverlight

Supported in: 5, 4, 3

Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.

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