[Math] Formula for homeomorphism between open annulus and punctured open disk

Question

Let $A$ be an open annulus. That is, let $0<r_1<r_2$ and let $A = \{p: r_1 < d(O,p) < r_2 \}$, where $O$ is the origin.

Let $P$ be the punctured open unit disk. That is, let $P = \{ p: d(O,p) \leq 1 \}\setminus\{O\}$.

I need help finding an explicit homeomorphism from $A$ to $P$, and its inverse.

Answer 1

Yes. But this sounds like homework, so I'll just give a hint: think in polar coordinates, and think simple.