What is the equivalent polar equation of $x^2 + (y-1)^2 = 1$? It's a question in the textbook that I have and I am having a hard time understanding it. How am I supposed to get the polar equation with this format?

Just substitute: $x = r\cos(\theta)$ and $y = r\sin(\theta)$:
\begin{align*}
r^2\cos^2(\theta) + (r\sin(\theta) - 1)^2 =& r^2\cos^2(\theta) + r^2\sin^2(\theta) - 2r\sin(\theta) + 1 = 1 \\
r^2 - 2r\sin(\theta) + 1 =& 1 \\
r^2 - 2r\sin(\theta) = 0 \\
r(r - 2\sin(\theta)) = 0 \\
r = 0, r = 2\sin(\theta)
\end{align*}
Well, clearly, $r = 0$ is not correct (it's only mathematically correct because of the equations), so this leaves: $r = 2\sin(\theta)$
