# Python math.atanh() Method

Musfirah Waseem Jan 30, 2023

Python `math.atanh()` method is an efficient way of calculating the inverse hyperbolic tangent of a number, x, in radians.

## Syntax of Python `math.atanh()` Method

``````math.atanh(x)
``````

### Parameters

`x` Any positive or negative value in the range -0.99 and 0.99.

### Return

The return type of this method is a float value representing the arctangent of `x`.

## Example Codes: Use `math.atanh()` Method in Python

``````import math

x = -0.9
value = math.atanh(x)
print(f"The inverse hyperbolic tangent of {x} is {value}.")

x = 0
value = math.atanh(x)
print(f"The inverse hyperbolic tangent of {x} is {value}.")

x = 0.0086
value = math.atanh(x)
print(f"The inverse hyperbolic tangent of {x} is {value}.")
``````

Output:

``````The inverse hyperbolic tangent of -0.9 is -1.4722194895832204.
The inverse hyperbolic tangent of 0 is 0.0.
The inverse hyperbolic tangent of 0.0086 is 0.008600212028075704.
``````

Note that the parameter should be a valid number. The values may be either positive or negative.

## Example Codes: Code Demonstrates an Error of the `math.atanh()` Method

``````import math

x = 1
value = math.atanh(x)
print(f"The inverse hyperbolic tangent of {x} is {value}.")
``````

Output:

``````Traceback (most recent call last):
File "main.py", line 5, in <module>
value=math.atanh(x)
ValueError: math domain error
``````

Note that a `TypeError` exception may occur if the argument value is not a float.

## Example Codes: Use the Equivalent of the `math.atanh()` Method

``````import math

x = 0.8
value = math.atanh(x)
print(f"The inverse hyperbolic tangent of {x} is {value}.")

equation = 0.5 * math.log((1 + x) / (1 - x))
print(f"Using the equation, the inverse hyperbolic tangent of {x} is {equation}.")
``````

Output:

``````The inverse hyperbolic tangent of 0.8 is 1.0986122886681098.
Using the equation, the inverse hyperbolic tangent of 0.8 is 1.0986122886681098.
``````

You can use either method to calculate the inverse hyperbolic tangent of a number.

Musfirah is a student of computer science from the best university in Pakistan. She has a knack for programming and everything related. She is a tech geek who loves to help people as much as possible.