How to find the angle between the Y+ axis and the line drawn to a point on the coordinate system?

Question

Mathematics

I drew as best I could :)

I can't find a solution to this problem, so I turn to you.
I need to find the Z angle, which is in this picture. X and Y values ​​from -1 to 1.

Thanks in advance!

Answer 1

Here it is easiest to use the scalar product . In this case, a unit vector along Y (a unit vector, since it's easier to calculate later), and the radius vector of a point. From the finished scalar product, you can find the cosine of the angle, and from it the angle itself

Answer 2

In the first quarter - atan(x/y).
In 2-3 - pi + atan(x/y)
In 4 - 2*pi + atan(x/y)