I´m getting the error, "atan2() takes exactly 2 arguments (1 given)"

Question

I´m new to programing so I have no idea what went wrong. please help

from math import atan2, pi
x = int(input("value of x"))
y = int(input("value of y"))
r = (x**2 + y**2) ** 0.5
ang = atan2(y/x)
print("Hypotenuse is", r, "angle is", ang)

Answer 1

The reason for that error is that atan2 requires two arguments. Observe:

>>> from math import atan, atan2
>>> atan(2)
1.1071487177940904
>>> atan2(4, 2)
1.1071487177940904

Note that atan(y/x) does not work if x is zero but atan2(y, x) will continue to work just fine:

>>> atan(4/0)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ZeroDivisionError: division by zero
>>> atan2(4, 0)
1.5707963267948966

Answer 2

In Python, there are 2 arctangent functions: atan is simply the inverse of tan; but atan2 takes 2 arguments. In your case since you know both catheti, you could as well use the 2-argument function atan2:

ang = atan2(y, x)

Alternatively, you might write

ang = atan(y / x)

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The rationale for atan2 is that it works correctly even if x is 0; while with atan(y / x) a ZeroDivisionError: float division by zero would be raised.

Additionally, atan can only give an angle between -π/2 ... +π/2, whereas atan2 knows the signs of both y and x, and thus can know which of the 4 quadrants the value falls to; its value ranges from -π to +π. Though, of course you wouldn't have a triangle with negative width or height...