Math.Cosh(Double) Method

Definition

Namespace:: System

Assemblies:: mscorlib.dll, System.Runtime.Extensions.dll

Assemblies:: netstandard.dll, System.Runtime.dll

Assembly:: System.Runtime.Extensions.dll

Assembly:: mscorlib.dll

Assembly:: netstandard.dll

Source:: Math.cs

Source:: Math.cs

Source:: Math.cs

Source:: Math.cs

Source:: Math.cs

Important

Some information relates to prerelease product that may be substantially modified before it’s released. Microsoft makes no warranties, express or implied, with respect to the information provided here.

Returns the hyperbolic cosine of the specified angle.

public:
 static double Cosh(double value);

public static double Cosh(double value);

static member Cosh : double -> double

Public Shared Function Cosh (value As Double) As Double

Parameters

value: Double

An angle, measured in radians.

Returns

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.

Examples

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
*/

// Example for the hyperbolic Math.Sinh( double )
// and Math.Cosh( double ) methods.
// In F#, the sinh and coh functions may be used instead
open System

// Evaluate hyperbolic identities with a given argument.
let useSinhCosh arg =
 let sinhArg = Math.Sinh arg
 let coshArg = Math.Cosh arg


 // Evaluate cosh^2(X) - sinh^2(X) = 1.
 printfn $"""
 Math.Sinh({arg}) = {Math.Sinh arg:E16}
 Math.Cosh({arg}) = {Math.Cosh arg:E16}"""
 printfn $"(Math.Cosh({arg}))^2 - (Math.Sinh({arg}))^2 = {coshArg * coshArg - sinhArg * sinhArg:E16}"

 // Evaluate sinh(2 * X) = 2 * sinh(X) * cosh(X).
 printfn $" Math.Sinh({2. * arg}) = {Math.Sinh(2. * arg):E16}"
 printfn $" 2 * Math.Sinh({arg}) * Math.Cosh({arg}) = {2. * sinhArg * coshArg:E16}"

 // Evaluate cosh(2 * X) = cosh^2(X) + sinh^2(X).
 printfn $" Math.Cosh({2. * arg}) = {Math.Cosh(2. * arg):E16}"
 printfn $"(Math.Cosh({arg}))^2 + (Math.Sinh({arg}))^2 = {coshArg * coshArg + sinhArg * sinhArg:E16}"

// Evaluate hyperbolic identities that are functions of two arguments.
let useTwoArgs argX argY =
 // Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
 printfn $"""
 Math.Sinh({argX}) * Math.Cosh({argY})
 Math.Cosh({argX}) * Math.Sinh({argY}) = {Math.Sinh argX * Math.Cosh argY + Math.Cosh argX * Math.Sinh argY:E16}"""
 
 printfn $" Math.Sinh({argX + argY}) = {Math.Sinh(argX + argY):E16}"

 // Evaluate cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y).
 printfn
 """Math.Cosh({argX}) * Math.Cosh({argY})
 Math.Sinh({argX}) * Math.Sinh({argY}) = {Math.Cosh argX * Math.Cosh argY + Math.Sinh argX * Math.Sinh argY:E16}"""
 
 printfn $" Math.Cosh({argX + argY}) = {Math.Cosh(argX + argY):E16}"

printfn
 """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)"""

useSinhCosh 0.1
useSinhCosh 1.2
useSinhCosh 4.9

printfn "\nEvaluate these hyperbolic identities with selected values for X and Y:"
printfn " sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y)"
printfn " cosh(X + Y) = cosh(X) * cosh(Y) + sinh(X) * sinh(Y)"

useTwoArgs 0.1 1.2
useTwoArgs 1.2 4.9

// 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.
Module SinhCosh
 
 Sub Main()
 Console.WriteLine( _
 "This example of hyperbolic " & _
 "Math.Sinh( Double ) and Math.Cosh( Double )" & vbCrLf & _
 "generates the following output." & vbCrLf)
 Console.WriteLine( _
 "Evaluate these hyperbolic identities " & _
 "with selected values for X:")
 Console.WriteLine( _
 " cosh^2(X) - sinh^2(X) = 1" & vbCrLf & _
 " 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( _
 vbCrLf & "Evaluate 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)
 End Sub
 
 ' Evaluate hyperbolic identities with a given argument.
 Sub UseSinhCosh(arg As Double)
 Dim sinhArg As Double = Math.Sinh(arg)
 Dim coshArg As Double = Math.Cosh(arg)
 
 ' Evaluate cosh^2(X) - sinh^2(X) = 1.
 Console.WriteLine( _
 vbCrLf & " Math.Sinh({0}) = {1:E16}" + _
 vbCrLf & " 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)

 End Sub
 
 ' Evaluate hyperbolic identities that are functions of two arguments.
 Sub UseTwoArgs(argX As Double, argY As Double)

 ' Evaluate sinh(X + Y) = sinh(X) * cosh(Y) + cosh(X) * sinh(Y).
 Console.WriteLine( _
 vbCrLf & " Math.Sinh({0}) * Math.Cosh({1}) +" + _
 vbCrLf & " 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}) +" + _
 vbCrLf & " 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)))

 End Sub
End Module '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

Remarks

The angle, value, must be in radians. Multiply by Math.PI/180 to convert degrees to radians.

This method calls into the underlying C runtime, and the exact result or valid input range may differ between different operating systems or architectures.

Applies to

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URL: https://learn.microsoft.com/en-us/dotnet/api/system.math.cosh?view=net-10.0