Given any Cartesian coordinates, (x,y), there are polar coordinates $(r,\theta)$ with $-\frac{\pi}{2} \lt \theta \le \frac{\pi}{2} .$
Find polar coordinates with $-\frac{\pi}{2} \lt \theta \le \frac{\pi}{2}$ for the following Cartesian coordinates:
(a) If $(x,y) = (5, 1)$ then $(r, \theta) = ($ , $)$,
(b) If $(x,y) = (12, -6)$ then $(r, \theta) = ($ , $)$,
(c) If $(x,y) = (-9, 5)$ then $(r, \theta) = ($ , $)$,
(d) If $(x,y) = (16, -2)$ then $(r, \theta) = ($ , $)$,
(e) If $(x,y) = (-1, 2)$ then $(r, \theta) = ($ , $)$,
(f) If $(x,y) = (0, -2)$ then $(r, \theta) = ($ , $)$.