Consider the function f:(r, t) e^r (cos(t), sin(t)). In particular, it maps the line (r0,t) to the circle of radius r0 (many times over).

Consider the function f:(r, t) → e^r (cos(t), sin(t)). In particular, it maps the line (r0,t) to the circle of radius r0 (many times over). Similarly, it maps the line (r,t0) to the ray (emanating at, but not containing, the origin) e^r(cos(t0), sin(t0)). Determine the image of the lines {(r0, t) : t} and {(r, t0) : r} under f.