Python cmath.cosh() Function

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The Python cmath.cosh() function returns the hyperbolic cosine of a given complex number.

The hyperbolic cosine function is denoted as cosh(x), where this is the mathematical function that calculates the value of the cosine complex number or a real number x. This function returns the real values that are greater than or equal to 1.

The mathematical representation of the hyperbolic cosine function is defined as −

cosh(x) = (ex + e-x)/ 2

Where e (e = 2.71828) is the base of the natural logarithm. This function is symmetric with respect to the y-axis; cosh(x) = cosh(-X).

Syntax

Following is the basic syntax of the Python cmath.cosh() function −

cmath.cosh(x)

Parameters

This function accepts real numbers, for which we need to find the hyperbolic cosine as a parameter.

Return Value

This function returns the hyperbolic cosine of the given number in the range of [1,).

Example 1

In the below example, we are calculating the hyperbolic cosine of positive numbers using cmath.cosh() function −

import cmath
x = 4.0
result = cmath.cosh(x)
print(result)

Output

Following is the output for the above code −

(27.308232836016487+0j)

Example 2

When we pass a fraction value to the cmath.cosh() function, then it returns a positive complex number −

import cmath
from fractions import Fraction 
x = Fraction(3, -5)
result = cmath.cosh(-x)
print(result)

Output

The output obtained is as follows −

(1.1854652182422676+0j)

Example 3

In the following example, we are retrieving the hyperbolic cosine of a negative number using the cmath.cosh() function.

import cmath
x = -0.67
result = cmath.cosh(x)
print(result)

Output

Following is the output of the above code −

(1.232972949211241-0j)

Example 4

Here, we are creating a loop to calculate the hyperbolic cosine values using the cmath.cosh() function. The loop will iterate through each value of a list.

import cmath
values = [3.0, 4.0, 7.0]
for x in values:
   result = cmath.cosh(x)
   print("cosh({}) = {}".format(x, result))

Output

Output is produced as shown below −

cosh(3.0) = (10.067661995777765+0j)
cosh(4.0) = (27.308232836016487+0j)
cosh(7.0) = (548.317035155212+0j)