Math.Cosh() Method in C#

The Math.Cosh() method in C# returns the hyperbolic cosine of a specified angle in radians. The hyperbolic cosine function is defined mathematically as cosh(x) = (e^x + e^(-x)) / 2, where e is Euler's number.

This method is commonly used in mathematical calculations involving hyperbolic functions, engineering applications, and statistical computations.

Syntax

Following is the syntax −

public static double Cosh(double value);

Parameters

• value − A double representing an angle measured in radians.

Return Value

Returns a double representing the hyperbolic cosine of the specified value. If the value is NaN (Not a Number), the method returns NaN. For positive or negative infinity, it returns positive infinity.

Using Math.Cosh() with Different Values

Example 1: Basic Usage

using System;

public class Demo {
   public static void Main() {
      double val1 = 0.0;
      double val2 = 1.0;
      double val3 = 2.0;
      
      Console.WriteLine("cosh(0) = " + Math.Cosh(val1));
      Console.WriteLine("cosh(1) = " + Math.Cosh(val2));
      Console.WriteLine("cosh(2) = " + Math.Cosh(val3));
   }
}

The output of the above code is −

cosh(0) = 1
cosh(1) = 1.54308063481524
cosh(2) = 3.76219569108363

Using Math.Cosh() with Negative Values

Example 2: Negative and Positive Values

using System;

public class Demo {
   public static void Main() {
      double positiveVal = 1.5;
      double negativeVal = -1.5;
      
      Console.WriteLine("cosh(1.5) = " + Math.Cosh(positiveVal));
      Console.WriteLine("cosh(-1.5) = " + Math.Cosh(negativeVal));
      Console.WriteLine("Are they equal? " + (Math.Cosh(positiveVal) == Math.Cosh(negativeVal)));
   }
}

The output of the above code is −

cosh(1.5) = 2.35240961524325
cosh(-1.5) = 2.35240961524325
Are they equal? True

Using Math.Cosh() with Special Values

Example 3: Special Cases

using System;

public class Demo {
   public static void Main() {
      Console.WriteLine("cosh(NaN) = " + Math.Cosh(double.NaN));
      Console.WriteLine("cosh(+?) = " + Math.Cosh(double.PositiveInfinity));
      Console.WriteLine("cosh(-?) = " + Math.Cosh(double.NegativeInfinity));
      Console.WriteLine("cosh(0) = " + Math.Cosh(0.0));
   }
}

The output of the above code is −

cosh(NaN) = NaN
cosh(+?) = ?
cosh(-?) = ?
cosh(0) = 1

Key Properties

Conclusion

The Math.Cosh() method calculates the hyperbolic cosine of a given angle in radians. It's an even function that always returns values ? 1, with its minimum value of 1 occurring at cosh(0). This method is essential for mathematical computations involving hyperbolic functions.