Let's simplify just a bit for illustration and take a cartesian grid in the +/+ quadrant. It's easily extended.
From the origin(0,0), for every (x,y) we can calculate two values:
- The radius -- the length of the line connecting the origin with (x,y)
- An angle from the ordinate at (0,x) to (x,y), conventionally called \theta
Which is a right triangle, r = \sqrt{x^{2} + y^{2}} and \theta = atan2(y,x)
(See the wiki
For your rotation, do you want to rotate the axes or the points? If you just want to rotate the axes, there's no need for the polar conversion. See Wolfram for an explanation of the straightforward matrix operations