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atan2() function in Python - GeeksforGeeks

Last Updated : 14 Mar, 2018

returns value of atan(y/x) in radians. The atan2() method returns a numeric value between -

and

representing the angle

of a (x, y) point and positive x-axis.

atan2(y, x)

(y, x) - Both must be a numeric value.

Returns atan(y / x), in radians.
The double value is \theta from polar coordinate (r, theta). 

Returns a TypeError if anything other than float is passed. 

# Python3 program to demonstrate
# the atan2() method 

# imports math 
import math

# prints the theta value of
# two negative co-ordinates 
theta1 = math.atan2(-0.9, -0.9) 
print("atan2(-0.9, -0.9) : ", theta1) 

# prints the theta value of
# two positive co-ordinates 
theta2 = math.atan2(1.2, 1.5) 
print("atan2(1.2, 1.5) : ", theta2) 

# prints the theta value of one
# positive and one negative co-ordinates 
theta3 = math.atan2(1.2, -1.5) 
print("atan2(1.2, -1.5):", theta3)

atan2(-0.5, -0.5): -2.356194490192345
atan2(1.2, 1.5): 0.6747409422235526
atan2(1.2, -1.5): 2.4668517113662407

# Python3 program to demonstrate the atan() method 

# imports math 
import math

# list containing x and y coordinates 
y = [1, 2, 3, 4] 
x = [6, 3, 7, 8] 

# traversing in range to get theta 
# for all y and x co-ordinates 
for i in range(len(x)):
    theta = math.atan2(y[i], x[i]) 
    print(theta) 

0.16514867741462683
0.5880026035475675
0.40489178628508343
0.4636476090008061

Program demonstrating the error

# Python3 program to demonstrate the  
# TypeError in atan() method 

# importing math 
import math

y, x = 3, 6

# when integer values are passed 
# it returns a TypeError
theta = math.atan2([y], [x]) 
print(theta)

Traceback (most recent call last):
  File "/home/622586ab389561bcdbfff258aca01e65.py", line 9, in 
    theta = math.atan2([y],[x]) 
TypeError: a float is required

This function is used to find the slope in radians when Y and X co-ordinates are given.

# Let's find the slope when X
# and Y co-ordinates are given 

# imports math 
import math

# X and Y are co-ordinates
X = 2; Y = 2 

# slope in radians 
theta1 = math.atan2(Y, X) 

# print the Slope in radians
print(theta1)

0.7853981633974483

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