Math.Cosh Method
.NET Framework 4.5
Returns the hyperbolic cosine of the specified angle.
Namespace: System
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 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 */
Windows 8, Windows Server 2012, Windows 7, Windows Vista SP2, Windows Server 2008 (Server Core Role not supported), Windows Server 2008 R2 (Server Core Role supported with SP1 or later; Itanium not supported)
The .NET Framework does not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.
