"Show that the polar equation $r = a \sin(t) + b \cos(t)$, where $ab \neq 0$, represents a circle, and find its center and radius."
I don't need the answer - I just need a hint to nudge me on. I've tried to tackle it by investigating tangents, completing squares, force-fitting into the formula of a circle, etc., but I can't seem to arrive at the indisputable conclusion that it must be a circle.
This is not homework, by the way. It comes from a Calculus textbook that I am studying on my own. I understand you have no reason to believe me, but if I were taking a real course, I'd bring this to my TA.