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Python cmath.asinh() Function

The Python cmath.asinh() function returns the inverse hyperbolic sine.

The inverse hyperbolic sine function is denoted as sinh^-1(x), or this function is also called arcsinh(x). If the value of x is between -1 and 1, the inverse sine function will return the angle whose sin is equal to x.

This function has a restricted domain, i.e., from the range [-,+].

Following is the basic syntax of the Python cmath.asinh() function −

cmath.asinh(x)

This function accepts a domain in the range of [-,+], for which we need to find the inverse of the hyperbolic sine as a parameter.

This function returns the inverse hyperbolic sine of the given number in the range of [-, +].

In hyperbolic trigonometry, the sine of 0 is equal to 0. When we pass '0' as an argument to the cmath.asinh() function, it returns 0j as the output.(Inverse hyperbolic sine of 0 is 0).

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

The output obtained is as follows −

0j

When we pass a fraction value to the cmath.asinh() function, then this returns a real number.

import cmath
from fractions import Fraction
x = Fraction(7, 9)
result = cmath.asinh(x)
print(result)

When we run the above code, it produces the following result −

(0.71522142246197+0j)

In the below example, we are passing a larger value, i.e., 1000 to the cmath.asinh() function.

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

The result obtained is given below −

(7.600902709541988+0j)

We are acquiring the inverse hyperbolic sine of a negative number by using the cmath.sinh() method.

import cmath
x = -4.0
result = cmath.asinh(x)
print(result)

Following is the output of the above code −

(-2.0947125472611012+0j

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