Python math.acos() Method

1. Syntax of Python math.acos() Method
2. Example Codes: Use Python math.acos() to Find Arccosine of a Value
3. Example Codes: Use Python math.acos() to Find Arccosine and Cosine

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

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

print(f"arccosine({1}) : {math.acos(1)} radians")
print(f"arccosine({-1}) : {math.acos(-1)} radians")
print(f"arccosine({-0.5}) : {math.acos(-0.5)} radians")
print(f"arccosine({0.5}) : {math.acos(0.5)} radians")
print(f"arccosine({0}) : {math.acos(0)} radians")

Output:

arccosine(1) : 0.0 radians
arccosine(-1) : 3.141592653589793 radians
arccosine(-0.5) : 2.0943951023931957 radians
arccosine(0.5) : 1.0471975511965979 radians
arccosine(0) : 1.5707963267948966 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.