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Python math.acos() Method

The Python math.acos() method computes the arc cosine of an angle, in radians.

The arc cosine of an angle is defined as the inverse of a cosine function. Therefore, the domain of the arc cosine function is the range of the cosine function, i.e., [-1, 1]; and its range is obtained in the form of radians. They can be converted into degrees using the degrees() method, if required.

Note − This function is not accessible directly, so we need to import math module and then we need to call this function using math static object.

Following is the syntax for the Python math.acos() method −

math.acos(x)

• x − This must be a numeric value in the range -1 to 1. If x is greater than 1 or less than -1, then it will generate an error.

This method returns arc cosine of x in radians.

The following example shows the usage of the Python math.acos() method. In here, we are trying to find the arc cosine values for the standard cosine values '0', '-1', and '1' using this method.

import math

zero = math.acos(0)
neg_one = math.acos(-1)
pos_one = math.acos(1)

print("Arc Cosine value of 0:", zero)
print("Arc Cosine value of -1:", neg_one)
print("Arc Cosine value of 1:", pos_one)

When we run above program, it produces following result −

Arc Cosine value of 0: 1.5707963267948966
Arc Cosine value of -1: 3.141592653589793
Arc Cosine value of 1: 0.0

Now let us try to convert the return values obtained from the method in the previous example into degrees using the degrees() method.

In this example, three objects containing the values 0, -1 and 1 are created. Using the acos() method, the arc cosine values of these objects are calculated in radians; which are later converted into degrees using the degrees() method

import math

zero = math.acos(0)
neg_one = math.acos(-1)
pos_one = math.acos(1)

print("Arc Cosine value of 0:", math.degrees(zero))
print("Arc Cosine value of -1:", math.degrees(neg_one))
print("Arc Cosine value of 1:", math.degrees(pos_one))

Once the program is executed, the output is produced as follows −

Arc Cosine value of 0: 90.0
Arc Cosine value of -1: 180.0
Arc Cosine value of 1: 0.0

The following example passes non-standard cosine ratios as arguments to this method; then the arc cosine values for these objects are calculated.

import math

acos1 = math.acos(0.64)
acos2 = math.acos(-0.97)

print("Arc Cosine value of 0.64:", acos1)
print("Arc Cosine value of -0.97:", acos2)

On compiling and executing the program above, the result is displayed as follows −

Arc Cosine value of 0.64: 0.8762980611683406
Arc Cosine value of -0.97: 2.896027136074501

However, if the arguments passed to this method exceed the value 1 or precede -1, a ValueError is raised.

import math

acos1 = math.acos(2)
acos2 = math.acos(-2)

print("Arc Cosine value of 2:", acos1)
print("Arc Cosine value of -2:", acos2)

If we compile and run the program, the output is produced as follows −

Traceback (most recent call last):
  File "main.py", line 3, in 
acos1 = math.acos(2)
ValueError: math domain error

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