Math.Cosh Method
[ This article is for Windows Phone 8 developers. If you’re developing for Windows 10, see the latest documentation. ]
Returns the hyperbolic cosine of the specified angle.
Assembly: mscorlib (in mscorlib.dll)
Parameters
- value
- Type: System.Double
An angle, measured in radians.
Return Value
Type: System.DoubleThe 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 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 */
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