How to know what a function in polar coordinates looks like

Question

So I was wondering if there are any good ways of figuring out how a function $r(\theta)$ looks like. Besides just trying out and plotting the points. In some simple cases we can show that $r=2\cos(\theta)$, for example, is a circle by showing it fulfills $(x-a)^2+(y-b)^2=R^2$. However, there are many other things than circles. For example the rose, $r=\cos(3\theta)$ how would you know how it looks like? Also, how would you find out the values of $\theta$ that bind one such petal?

Answer 1

Well for starters, $r=\sin(\frac 1{\theta})$ looks like a mouse's face: