I'm using angles because I'm using vectors and not keeping track of individual x- and y- axis motion, but rather speed in a direction. The use of angles also gives me the possibility of using angles other than right angles, e.g. 45- and 22.5-degree ramps. (I'm hoping to get to ramps in the future, but at the moment I'm only worrying about 90-degree angles; I'm just trying to write it so that it's easy to port later.)
EDIT: I forgot to mention the whole division thing: That's exactly what it is, and I can't believe I didn't realize that. I'll let you know if correcting that fixes the problem.
PS: I hate the quick edit feature. XD