Math.Sinh() Method in C#

The Math.Sinh() method in C# calculates the hyperbolic sine of a specified angle in radians. The hyperbolic sine function is defined mathematically as (e^x - e^-x)/2, where e is Euler's number (approximately 2.71828).

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

Syntax

Following is the syntax of the Math.Sinh() method −

public static double Sinh(double value)

Parameters

value: A double-precision floating-point number representing an angle in radians for which the hyperbolic sine is to be calculated.

Return Value

Returns a double representing the hyperbolic sine of the specified angle. The method returns:

• NegativeInfinity if the value is NegativeInfinity

• PositiveInfinity if the value is PositiveInfinity

• NaN if the value is NaN

Example with Large Values

This example demonstrates the Math.Sinh() method with larger angle values −

using System;

public class Demo {
    public static void Main() {
        double val1 = 30.0;
        double val2 = 45.0;
        
        Console.WriteLine("sinh(30.0) = " + Math.Sinh(val1));
        Console.WriteLine("sinh(45.0) = " + Math.Sinh(val2));
    }
}

The output of the above code is −

sinh(30.0) = 5343237290762.23
sinh(45.0) = 1.74671355287425E+19

Example with Small Values

This example shows the behavior of Math.Sinh() with smaller values including zero −

using System;

public class Demo {
    public static void Main() {
        double val1 = 0.0;
        double val2 = 1.1;
        double val3 = -1.5;
        
        Console.WriteLine("sinh(0.0) = " + Math.Sinh(val1));
        Console.WriteLine("sinh(1.1) = " + Math.Sinh(val2));
        Console.WriteLine("sinh(-1.5) = " + Math.Sinh(val3));
    }
}

The output of the above code is −

sinh(0.0) = 0
sinh(1.1) = 1.33564747012418
sinh(-1.5) = -2.12927945509482

Example with Special Values

This example demonstrates how Math.Sinh() handles special floating-point values −

using System;

public class Demo {
    public static void Main() {
        Console.WriteLine("sinh(Infinity) = " + Math.Sinh(Double.PositiveInfinity));
        Console.WriteLine("sinh(-Infinity) = " + Math.Sinh(Double.NegativeInfinity));
        Console.WriteLine("sinh(NaN) = " + Math.Sinh(Double.NaN));
        Console.WriteLine("sinh(1) = " + Math.Sinh(1.0));
    }
}

The output of the above code is −

sinh(Infinity) = Infinity
sinh(-Infinity) = -Infinity
sinh(NaN) = NaN
sinh(1) = 1.1752011936438

Conclusion

The Math.Sinh() method in C# calculates the hyperbolic sine of an angle in radians, returning a double value. It handles special cases like infinity and NaN appropriately, making it suitable for mathematical and scientific calculations involving hyperbolic functions.