How to manage hyperbolic functions in Python

By Sai Prasanna

First, let us see the basic definition of the function. “A function is a block of organized code that performs some specific task.”

In this tutorial, we are going to study about the hyperbolic functions of math module on complex numbers in Python.

Many built-in functions are defined in the math module, and they can be used for any of Python calculations like hyperbolic calculations.

First of all, let us perform the basic trigonometric functions sin, cos, tan functions. These functions will return the sin, cosine, tangent of a given number as an argument. Consider the example.

import math
x=1.25
print("sin value is:",math.sin(x))
print("cos value is:",math.cos(x))
print("tan value is:",math.tan(x))

Output :

sin value is: 0.9489846193555862
cos value is: 0.3153223623952687
tan value is: 3.0095696738628313

Example On complex numbers

import cmath
x=1.5
y=1.5
#converting x and y to complex number z
z=complex(x,y)
print("Sin value of complex number is:",end="")
print(cmath.sin(z))
print("cos value of complex number is:",end="")
print(cmath.cos(z))
print("tan value of complex number is:",end="")
print(cmath.tan(z)

Here in the above code, we have utilized the cmath library. The cmath helps us to handle the mathematical functions for complex numbers in Python. And this module accepts the integers, floating-point numbers or complex numbers as arguments.

This complex number is represented by x+iy where x and y are the real numbers. We can convert these two real numbers into complex numbers by utilizing the complex function as shown in the above code.

Output :

The sine value of complex number is:(2.3465167976443118+0.15061927022193866j)
The cos value of complex number is:(0.16640287335850498-2.1239455815360935j)
The tan value of complex number is:(0.01554584115148238+1.1035734368075185j)

import cmath
x=1.5
y=1.5
#converting x and y to complex number z
z=complex(x,y)
print("The hyperbolic sine of complex number is:",end="")
print(cmath.sinh(z))
print("The hyperbolic cos of complex number is:",end="")
print(cmath.cosh(z))
print("The hyperbolic tan of complex number is:",end="")
print(cmath.tanh(z))

The hyperbolic sine of complex number is:(0.15061927022193866+2.3465167976443118j)
The hyperbolic cos of complex number is:(0.16640287335850498+2.1239455815360935j)
The hyperbolic tan of complex number is:(1.1035734368075185+0.01554584115148238j)

import cmath
x="1.25"
print(cmath.sinh(x))
print(cmath.cosh(x))
print(Cmath.tanh(x))

TypeError: must be real number, not str

import cmath
x=1.5
y=1.5
z=complex(x,y)
print("The inverse hyperbolic sine of complex number is",end="")
print(cmath.asinh(z))
print("The inverse hyperbolic cos of complex number is",end="")
print(cmath.acosh(z))
print("The inverse hyperbolic tan of complex number is",end="")
print(cmath.atanh(z))

The inverse hyperbolic sine of complex number is:(1.44973434958536+0.7304012179532257j)
The inverse hyperbolic cos of complex number is:(1.44973434958536+0.8403951088416709j)
The inverse hyperbolic tan of complex number is:(0.3059438579055289+1.2164831907310616j)