# Python math.acos() Method

Python has a built-in math module specifically for performing mathematics operations. Additionally, it also supports trigonometric and inverse trigonometric functions.

The inverse of cosine is known as arccosine or `cos⁻¹θ`. Theoretically, the cosine of an angle `θ` is the ratio of its adjacent side and the hypotenuse and the domain and range of arccosine are `[-1, 1]` and `[0, π]`, respectively.

``````cos(θ) = (adjacent side) / (hypotenuse)
arccosine(θ) = cos⁻¹((adjacent side) / (hypotenuse))
``````

This article will discuss the `acos()` method from the math module that helps calculate arccosine for angles.

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

``````math.acos(x)
``````

### Parameters

Type Description
`x` Integer A value between -1 and 1, both inclusive.

### Returns

The `acos()` method returns the inverse of cosine or arccosine of `x` in radians. The result is between the range `0` and `π`, both inclusive.

## Example Codes: Use Python `math.acos()` to Find Arccosine of a Value

``````import math

``````

Output:

``````arccosine(1) : 0.0 radians
``````

The code above computes the inverse of cosine or arccosine for `1`, `-1`, `-0.5`, `0.5`, and `0`. All the results are in the range `[0, π]`.

## Example Codes: Use Python `math.acos()` to Find Arccosine and Cosine

``````import math

x = -1
acos = math.acos(x)
print(f"arccosine({x}):", acos)
print(f"cos({acos}):", math.cos(acos))
x = 0
acos = math.acos(x)
print(f"arccosine({x}):", acos)
print(f"cos({acos}):", math.cos(acos))
x = 1
acos = math.acos(x)
print(f"arccosine({x}):", acos)
print(f"cos({acos}):", math.cos(acos))
``````

Output:

``````arccosine(-1): 3.141592653589793
cos(3.141592653589793): -1.0
arccosine(0): 1.5707963267948966
cos(1.5707963267948966): 6.123233995736766e-17
arccosine(1): 0.0
cos(0.0): 1.0
``````

The code above calculates the arccosine of some value `x` and uses its result to re-compute `x` using cosine. It performs the above operation for three values, `-1`, `0`, and `1`.

Note that for `x = 0`, the cosine output is `6.123233995736766e-17`, which is a minimal value and close to zero. Generally, such values are approximated to the nearest integer for simplicity’s sake, which is, in this case, `0`.

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.