Get the Trigonometric inverse cosine in Python

The inverse cosine (arccos) is a multivalued function that returns the angle whose cosine equals a given value. In NumPy, the arccos() function returns angles in the range [0, ?] radians. For real-valued inputs, it always returns real output, while invalid values (outside [-1, 1]) return nan.

To find the trigonometric inverse cosine, use the numpy.arccos() method. The method returns the angle of the array intersecting the unit circle at the given x-coordinate in radians [0, ?].

Syntax

numpy.arccos(x, out=None, where=True)

Parameters

The function accepts the following parameters ?

• x ? The x-coordinate on the unit circle. For real arguments, the domain is [-1, 1]
• out (optional) ? A location into which the result is stored
• where (optional) ? Condition to broadcast over the input

Basic Examples

Let's find the inverse cosine for common values ?

import numpy as np

# Finding arccos for boundary values
print("arccos(1):", np.arccos(1))
print("arccos(-1):", np.arccos(-1))
print("arccos(0):", np.arccos(0))
print("arccos(0.5):", np.arccos(0.5))

arccos(1): 0.0
arccos(-1): 3.141592653589793
arccos(0): 1.5707963267948966
arccos(0.5): 1.0471975511965979

Working with Arrays

The function also works with NumPy arrays ?

import numpy as np

# Array of cosine values
values = np.array([1, 0.5, 0, -0.5, -1])
angles = np.arccos(values)

print("Input values:", values)
print("Arccos angles (radians):", angles)
print("Arccos angles (degrees):", np.degrees(angles))

Input values: [ 1.   0.5  0.  -0.5 -1. ]
Arccos angles (radians): [0.         1.04719755 1.57079633 2.0943951  3.14159265]
Arccos angles (degrees): [  0.  60.  90. 120. 180.]

Handling Invalid Input

Values outside the domain [-1, 1] return nan ?

import numpy as np

# Testing with invalid values
invalid_values = np.array([1.5, -2, 0.8])
result = np.arccos(invalid_values)

print("Input:", invalid_values)
print("Result:", result)

Input: [ 1.5 -2.   0.8]
Result: [       nan        nan 0.64350111]

Common Use Cases

Conclusion

The numpy.arccos() function calculates inverse cosine values, returning angles in radians within [0, ?]. Use np.degrees() to convert results to degrees when needed.