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The Python math.asinh() method returns the inverse hyperbolic sine of a given number.

The inverse sine method, denoted as sinh^-1(x) or sometimes as arcsinh(x), is a mathematical method that retrieves the angle whose sine is a given number x. In other words, if you have a value x between -1 and 1, the inverse sine method will return the angle (in radians) whose sine equals x.

Mathematically, this is expressed as −

sinh-1(x) = angle Θ such that sinh(Θ) = x

This method has a restricted domain and the range of [-∞, +∞].

Syntax

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

math.asinh(x)

Parameters

This method accepts a number in the domain of [-∞ to +∞] for which you want to find the inverse hyperbolic sine as a parameter.

Return Value

The method returns the inverse hyperbolic sine of the given number in the range of [-∞ to +∞].

Example 1

The hyperbolic sine of 0 is 0. Therefore, when we pass 0 as an argument to math.asinh() method, it returns 0.0 −

import math
x = 0
result = math.asinh(x)
print(result) 

Output

The output obtained is as follows −

0.0

Example 2

If we pass a fraction value to the math.asinh() method, it returns a real number −

import math
from fractions import Fraction
x = Fraction(5, 4)
result = math.asinh(x)
print(result)  

Output

Following is the output of the above code −

1.0475930126492587

Example 3

In the following example, we are passing a larger value "1000" to the math.asinh() method −

import math
x = 1000
result = math.asinh(x)
print(result) 

Output

The result produced is as shown below −

7.600902709541988

Example 4

In here, we are retrieving the inverse hyperbolic sine of a negative number using the math.asinh() method −

import math
x = -2.0
result = math.asinh(x)
print(result)  

Output

We get the output as shown below −

-1.4436354751788103

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