I am trying to make some data work for Malus Law with 3 polarizers (don't worry, my question is about geometry, not physics), and I think I should know this but I'm loosing my mind at this point.
Let's say we have a vector $v$ in two dimensions making an angle $\theta$ with the $Y$ axis, then what's the expresion for the angle with the $X$ axis?
I was thinking about adding something to $\theta$, but I believe that doesn't work for a domain $[0,2\pi]$.
Do this using coordinates:
$x = ||v||\sin(\theta)$
$y = ||v||\cos(\theta)$
Then your angle with the x Axis is $\phi = atan2(y, x)$ where atan2 is the arc tangent corrected for the quadrant by considering the sign of x and y.