atanh() math function to get inverse hyperbolic tangent of x input number in radian in Python

atanh(x) returns inverse hyperbolic tangent of x , the input number x is in radian.

import math
print(math.atanh(-0.9))  # -1.4722194895832204
print(math.atanh(0))     # 0.0
print(math.atanh(0.9))   # 1.4722194895832204

Note that all the inputs are in radian.
less than or equal to -1 or more than equal to 1 , we will get ValueError

import math
print(math.atanh(1.0))

Above code will generate error.

Inputs in degree

We can convert radian value to degree and use the same

import math
in_degree = 50
in_redian = math.radians(in_degree)
print(math.atanh(in_redian)) # 1.344146641636003

Output

1.344146641636003

1 radian = 57.2957914331 degree
1 degree = 0.0174533 radian

Drawing graph of atanh()

We will use Matplotlib to generate graph of atanh $atanh graph$

import matplotlib.pyplot as plt
x=[]
y=[]
i=-0.99
while (i<1):
    x.append(i)
    y.append(math.atanh(i))
    i=i+0.01
plt.plot(x,y)
plt.axvline(x=0.00,linewidth=2, color='#f1f1f1')
plt.axhline(y=0.00,linewidth=2, color='#f1f1f1')
plt.grid(linestyle='-',
    linewidth=0.5,color='#f1f1f1')
plt.show()

Example 1: Handling Out of Range Values

import math
try:
    print(math.atanh(1.5))  # Raises ValueError
except ValueError as e:
    print(e)

Output

math domain error

Example 2: Using atanh() in Engineering Calculations

import math
signal = 0.5  # A signal amplitude example
result = math.atanh(signal)
print(result)  # Output: 0.5493061443340548

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Subhendu Mohapatra

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