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?

I would expand 
$(y-1)^2\to y^2-2y+1$
, making the equation 
$x^2+y^2-2y+1=1$
, which simplifies to 
$x^2+y^2=2y$
. 
$x^2+y^2$
 can be replaced by 
$r^2$
, and 
$y$
 can be replaced by 
$r\sin\theta$
, so 
$r^2=2r\sin\theta$
.
