Efficiently find points inside a circle sector

Question

I have a set of 2d points distributed randomly. I need to perform a time intensive operation on a small subset of these points but I need to first figure out what points I n

Answer 1

I know you don't want trigonometry, but you could convert each point (in your subset) to its polar coordinates (where the origin is your specific point) and threshold r,theta where r < R and T1 < theta < T2 corresponding to the sector. It's certainly memory efficient!