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Python math.tanh() Method

The Python math.tanh() method returns the hyperbolic tangent of a given number.

The hyperbolic tangent method, denoted as tanh(x), is a mathematical method that calculates the value of the tangent of a complex number or a real number x. It returns real values that range between -1 and 1.

Mathematically, the hyperbolic tangent method is defined as −

tanh(x) = sinh(x)/ cosh(x)

Where, sinh(x) is the hyperbolic sine method and cosh(x) is the hyperbolic cosine method. This method is odd, meaning that tanh(-x) = -tanh(x).

Following is the basic syntax of the Python math.tanh() method −

math.tanh(x)

This method accepts a number (all real numbers) for which you want to find the hyperbolic tangent as a parameter.

The method returns the hyperbolic tangent of the given number in the range of (-1, 1).

In the following example, we calculate the hyperbolic tangent of a positive number using the math.tanh() method −

import math
x = 2.0
result = math.tanh(x)
print(result) 

The output obtained is as follows −

0.9640275800758169

If we pass a fraction value to the math.tanh() method, it returns a number between -1 and 1 (exclusive) −

import math
from fractions import Fraction
x = Fraction(5, -9)
result = math.tanh(x)
print(result) 

Following is the output of the above code −

-0.5046723977218567

In here, we are retrieving the hyperbolic tangent of a negative number using the math.tanh() method −

import math
x = -0.5
result = math.tanh(x)
print(result)  

We get the output as shown below −

-0.46211715726000974

In this example, we use a loop to calculate the hyperbolic tangent of multiple values using the math.tanh() method. The loop iterates through each value in the values list, calculates the hyperbolic tangent, and prints the result for each value −

import math
values = [1.0, 2.0, 3.0]
for x in values:
   result = math.tanh(x)
   print("tanh({}) = {}".format(x, result))

The result produced is as shown below −

tanh(1.0) = 0.7615941559557649
tanh(2.0) = 0.9640275800758169
tanh(3.0) = 0.9950547536867305

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