求Python中的一条线段与y轴的夹角

Question

Ive been trying to figure this out but I just can quite get it right. I have the following coordinate plane.

If I have a segment coming off of the origin like either of the two segments shown below, how can I find that angle between the segment and the Y axis? The only input I have is the endpoint (x, y) of one of the segments

I will not have two segments in the plane at the same time though, so finding the total angle between the two segments will not work. I will only ever have one segment on the coordinate plane at one time.

Answer 1

You need the atan2 function from the math module:

from math import atan2,pi

atan2(y,x)*180/pi # in degrees, positive angles are counter clockwise

for x in range (-1,2):
    for y in range(-1,2):
        print((x,y),atan2(y,x)*180/pi)

(-1, -1) -135.0
(-1, 0)   180.0
(-1, 1)   135.0
(0, -1)   -90.0
(0, 0)      0.0
(0, 1)     90.0
(1, -1)   -45.0
(1, 0)      0.0
(1, 1)     45.0

Answer 2

Do you know the lengths of any of the sides? If so, you could use the known angle of 90 degrees (because those are right triangles) to deduce the unknown angle. This could be done with the Law of Sin or Law of Cos depending on the information known.

Answer 3

You need to take the inverse tangent of x ÷ y and import the math module. In Python, it would look like this:

import math

theta = math.degrees(math.atan(x / y)) # Also convert the answer from radians to degrees