# Python math.acosh() Method

Vaibhav Vaibhav Jan 30, 2023

Python has a built-in library named `math` for performing many mathematical operations. Fortunately, this library also supports trigonometric and inverse trigonometric operations.

The inverse of a hyperbolic cosine is known as inverse hyperbolic cosine or `cosh⁻¹θ`. Its domain is the closed interval `[1, +∞)`.

``````arcosh(θ) = ln(θ + √(θ² - 1))
``````

This article will discuss the `acosh()` method from the math module that helps compute inverse hyperbolic cosine for angles.

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

``````math.acosh(x)
``````

### Parameters

Type Explanation
`x` Integer A value between 1 and ∞, 1 inclusive.

### Returns

The `acosh()` method returns the inverse hyperbolic cosine or `cosh⁻¹` of `x` in radians. The result is between the range `0` and `∞`, including `0`.

## Example Codes: Use Python `math.acosh()` to Compute Inverse Hyperbolic Cosine of a Value

``````import math

``````

Output:

``````cosh⁻¹(1) : 0.0 radians
``````

The Python code above computes the inverse of cosine or arccosine for `1`, `10`, `200`, `5000`, and `99999`. Note that all the results are in the range `[0, ∞)`.

## Example Codes: Use Python `math.acosh()` to Compute Arccosine and Cosine

``````import math

inputs = [1, 10, 200, 5000, 99999]

for x in inputs:
acosh = math.acosh(x)
print(f"cosh⁻¹({x}):", acosh)
print(f"cosh({acosh}):", math.cosh(acosh))
``````

Output:

``````cosh⁻¹(1): 0.0
cosh(0.0): 1.0
cosh⁻¹(10): 2.993222846126381
cosh(2.993222846126381): 9.999999999999998
cosh⁻¹(200): 5.9914582970493875
cosh(5.9914582970493875): 200.0
cosh⁻¹(5000): 9.210340361976183
cosh(9.210340361976183): 5000.000000000001
cosh⁻¹(99999): 12.206062645455173
cosh(12.206062645455173): 99999.00000000001
``````

The Python code above calculates inverse hyperbolic cosine of some value `x` and uses its result to re-compute `x` using hyperbolic cosine. It performs the above operation for `1`, `10`, `200`, `5000`, and `99999`.

Vaibhav is an artificial intelligence and cloud computing stan. He likes to build end-to-end full-stack web and mobile applications. Besides computer science and technology, he loves playing cricket and badminton, going on bike rides, and doodling.