# Python math.cos and math.acos function

## Math.cos() function

In Python, the Math module is used for performing the mathematical operations. It includes the math.cos() function that is used for obtaining the cosine value of an angle in radians.

Syntax:

math.cos(x)

Parameter:

x : Numeric value

Returns: Returns the cosine value of an angle.

Example:

import math

a = math.pi / 6

# returns the cosine value

print ("cosine value of pi / 6 is: ", end ="")

print (math.cos(a))

Output:

cosine value of pi/6 is: 0.8660254037844387

Example 2:

import math

print ("cos(-1.23) : ", math.cos(-1.23))

print ("cos(3) : ", math.cos(3))

print ("cos(10) : ", math.cos(10))

print ("cos(pi/3) : ", math.cos(math.pi/3))

print ("cos(math.pi) : ", math.cos(math.pi))

print ("cos(2*math.pi) : ", math.cos(2*math.pi))

Output:

cos(-1.23) : 0.3342377271245026

cos(3) : -0.9899924966004454

cos(10) : -0.8390715290764524

cos(pi/3) : 0.5000000000000001

cos(math.pi) : -1.0

cos(2*math.pi) : 1.0

We can also obtain the graphical representation of the cos function by using the matplotlib and Numpy libraries.

Example:

import math

import numpy as np

import matplotlib.pyplot as plt

input_arr = np.linspace(-(2 * np.pi), 2 * np.pi, 20)

out_arr = []

for i in range(len(input_arr)):

out_arr.append(math.cos(input_arr[i]))

i += 1

print("input_arr : ", input_arr)

print("\nout_arr : ", out_arr)

plt.plot(input_arr, out_arr, color='red', marker="o")

plt.title("math.cos()")

plt.xlabel("X")

plt.ylabel("Y")

plt.show()

Output:

## Python math.acos()

If we want to find the inverse of cosine then the math.acos() function is used for finding the inverse of cos.

It returns the arc cosine for the particularized expression. The value between -1 to 1 should be passed in this function.

Syntax

math.acos(x)

Parameter: Only a single parameter is accepted.

x : Numeric valuee to be passed to math.acos()

Returns: It returns arc cosine value.

Example:

import math

a = math.pi / 4

# returns the value

print ("The value of arc cosine of pi / 4 is: ", end ="")

print (math.acos(a))

Output:

The value of arc cosine of pi / 4 is: 0.6674572160283838

Example 2:

import math

print ("acos(0.64) : ", math.acos(0.64))

print ("acos(0) : ", math.acos(0))

print ("acos(-1) : ", math.acos(-1))

print ("acos(1) : ", math.acos(1))

print ("acos(0.75) : ", math.acos(0.75))

print ("acos(0.99) : ", math.acos(0.99))

print ("acos(pi/4) : ", math.acos(math.pi/4))

Output:

acos(0.64) : 0.8762980611683406

acos(0) : 1.5707963267948966

acos(-1) : 3.141592653589793

acos(1) : 0.0

acos(0.75) : 0.7227342478134157

acos(0.99) : 0.1415394733244273

acos(pi/4) : 0.6674572160283838

Example 3:

The arc cosine values of different data types can be found with the math.acos() function.

Now, we can understand by taking an example.

import math

Tup = (0.21, 0.12, 0.39, -0.89 , 0.42) # Declaration of tuple

Lis = [-0.1, 0.92, 0.35, -0.46 , 0.85] # Declaration of list

print('Arc Cosine value of Positive Number = %.2f' %math.acos(1))

print('Arc Cosine value of Negative Number = %.2f' %math.acos(-1))

print('Arc Cosine value of Tuple Item = %.2f' %math.acos(Tup[3]))

print('Arc Cosine value of List Item = %.2f' %math.acos(Lis[2]))

print('Arc Cosine value of Multiple Number = %.2f' %math.acos(0.10 + 0.20 - 0.40))

Output:

Arc Cosine value of Positive number = 0.00

Arc Cosine value of Negative Number x = 9.14

Arc Cosine value of Tuple Item =2*6

Arc Cosine value of List Item = 1.21

Arc Cosine value of Multiple number = 1.67

Example:

We can also obtain the graphical representation of the acos function by using the matplotlib and Numpy libraries.

import math

import numpy as np

import matplotlib.pyplot as plt

in_array = np.linspace(-(1 / 3.5 * np.pi), 1 / 3.5 * np.pi, 20)

out_array = []

for i in range(len(in_array)):

out_array.append(math.acos(in_array[i]))

i += 1

print("Input_Array : \n", in_array)

print("\nOutput_Array : \n", out_array)

plt.plot(in_array, out_array, "go-")

plt.title("math.acos()")

plt.xlabel("X")

plt.ylabel("Y")

plt.show()

Output:

## Conclusion

In the above article, We studied Python math.cos() function and also math.acos() function and we learned how to use these two  functions in Python.