acos() math function to get arc cosine of input number in radian in Python

acos(x) returns arc cosine of x , the input number x is in radian.

import math
print(math.acos(1))     # 0.0
print(math.acos(0.56))  # 0.9764105267938343
print(math.acos(-0.56)) # 2.165182126795959
print(math.acos(-1))    # 3.141592653589793
print(math.acos(0))     # 1.5707963267948966

Note that all the inputs are in radian.
For any value more than 1 or less than -1 , we will get ValueError

print(math.acos(1.01))
print(math.acos(-1.01))

Above code will generate error.

Inputs in degree

We can convert radian value to degree and use the same

import math
in_degree = 57
in_redian = math.radians(in_degree)
print(math.acos(in_redian))

Output

0.10165406130640683

1 radian = 57.2957914331 degree
1 degree = 0.0174533 radian

Drawing graph of acos()

In our Trigonometric language acos is also know as arccos. Using this we will use Matplotlib to generate graph of acos $acos graph$

import matplotlib.pyplot as plt
import math
x=[]
y=[]
i=-1
while (i<=1):
    x.append(i)
    y.append(math.acos(i))
    i=i+0.01
plt.plot(x,y)    
plt.show()

Example 1: Handling Invalid Inputs

import math
try:
    print(math.acos(1.5))  # Will raise ValueError
except ValueError as e:
    print(e)  # Output: math domain error

Example 2: Calculating Angles in a Triangle

import math
a, b, c = 3, 4, 5  # sides of the triangle
angle_C = math.acos((a**2 + b**2 - c**2) / (2 * a * b))
print(math.degrees(angle_C))  # Output: 90.0 (degrees)

Example 3: Using acos() to Find an Angle in Radians

import math
cos_value = 0.5
angle = math.acos(cos_value)
print(angle)  # Output: 1.0471975511965979 (in radians)

Example 4: Comparing acos() with cos()

import math
cos_value = math.cos(math.pi / 3)  # cos(60 degrees)
angle = math.acos(cos_value)
print(angle)  # Output: 1.0471975511965979 (radians, which is 60 degrees)

Example 5: Using acos() for Physics Calculations

import math
force_angle_cos = 0.866  # Cosine of angle between two forces
angle = math.acos(force_angle_cos)
print(math.degrees(angle))  # Output: 30 degrees

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Subhendu Mohapatra

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