Convert to polar coordinates, where 0 degrees means x = 0 and y > 0, increasing clockwise.

Question

This isn't terribly different from from regular conversion to polar, but I'm having trouble adapting it. The results I'm looking for are in the range [0,360) that adhere to the following example data.

 x |  y | Deg
-------------    
 0 |  1 |   0 (North)
-------------
 1 |  0 |  90 (East)
-------------
 0 | -1 | 180 (South)
-------------
-1 |  0 | 270 (West)

x and y are the result of subtracting two coordinates. This is for a program I'm writing, so feel free to break it down into "if this then that" calculations.

Answer 1

This is the same as the usual definition of polar coordinates, except with the roles of $x$ and $y$ interchanged. So: $$ x = r \sin \theta\\ y = r \cos \theta $$ and in the opposite direction: $$ r = \sqrt{x^2 + y^2}\\ \theta = \operatorname{atan2}(x,y) $$ I think that in most programming languages $\operatorname{atan2}$ produces a value in the range $(-\pi,\pi]$, so to convert to degrees you should multiply by $180/\pi$ and add $360$ if the result is negative to get into the range $[0,360)$.