Learning to graph polar equations, and I'm trying to figure out how periodicity applies. The equation that I am graphing is $\displaystyle r = \sin(5\theta)$.

So, I know that the periodicity of this graph is $\displaystyle \frac{2\pi}{5}$. Easy enough (I think).

But where I am confused is that when I graph this, I have to graph angles up to $\displaystyle \pi$ before the graph completes. I expected that there would be a relationship between the periodicity of the equation when graphed in Cartesian coordinates and the graph in polar coordinates.

How do I determine how many angles I need to calculate before the graph is complete?