C++ cmath cosh() Function

The C++ cmath cosh() function computes the hyperbolic cosine of an angle specified in radians. This is defined mathematically as the average of the exponential of the number and its negative: (exp(number) + exp(-number)) / 2.

It is commonly used in various mathematical and engineering applications that involve trigonometric and hyperbolic functions, and it works with different types of floating-point numbers.

Syntax

Following is the syntax for C++ cmath cosh() function.

double cosh(double x);
or
float cosh(float x);
or
long double cosh(long double x);

Parameters

• x - The value representing a hyperbolic angle.

Return Value

The function returns the hyperbolic cosine of the given angle, as a floating-point value.

Time Complexity

The time complexity of this function is constant, i.e.,O(1).

Example 1

In the following example, we calculate the hyperbolic cosine of a given angle in radians using cosh() function.

#include <iostream>
#include <cmath>
int main() {
   double angle = 0.5;
   std::cout << "Hyperbolic cosine of 0.5 radians: " << std::cosh(angle) << std::endl;
   return 0;
}

Output

If we run the above code it will generate the following output −

Hyperbolic cosine of 0.5 radians: 1.12763

Example 2

In this example, we are going to calculate the hyperbolic cosine of an angle in degrees by first converting the angle to radians.

#include <iostream>
#include <cmath>
int main() {
   double angle_degrees = 30.0;
   double angle_radians = angle_degrees * (M_PI / 180.0);
   std::cout << "Hyperbolic cosine of 30 degrees: " << std::cosh(angle_radians) << std::endl;
   return 0;
}

Output

Following is the output of the above code −

Hyperbolic cosine of 30 degrees: 1.14024

Example 3

This example demonstrates the use of the std::cosh function in a loop to calculate and display the hyperbolic cosine values for angles ranging from 0 to , using increments of /6 radians.

#include <iostream>
#include <cmath>
int main() {
   for (double angle = 0.0; angle <= M_PI; angle += M_PI / 6) {
      std::cout << "Hyperbolic cosine of " << angle << " radians: " << std::cosh(angle) << std::endl;
   }
   return 0;
}

Output

Output of the above code is as follows −

Hyperbolic cosine of 0 radians: 1
Hyperbolic cosine of 0.523599 radians: 1.14024
Hyperbolic cosine of 1.0472 radians: 1.60029
Hyperbolic cosine of 1.5708 radians: 2.50918
Hyperbolic cosine of 2.0944 radians: 4.12196
Hyperbolic cosine of 2.618 radians: 7.42032
Hyperbolic cosine of 3.14159 radians: 11.5919