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Math.Cosh Method

Returns the hyperbolic cosine of the specified angle.

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

[SecuritySafeCriticalAttribute]
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 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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