A need to show that the curve given in polar equation $\mathbb{r=a\sin(b\theta)}$ is an algebraic curve if $b=\frac{m}{n}$, $m,n\in \mathbb{N}^{*}$ and $(m,n)=1$. Also I am supposed to find the polynomial which it satisfies. If $b$ is an irrational number then the curve (I don't know the name in English) is not algebraic.
I would appreciate any help with this problem.
PS. I've studied Algebraic Curves, Commutative Algebra and Algebraic Geometry many years ago (7 years to be exact!). So, I am trying get back to business. If it is a silly question, please delete it.