Shape of the polar curve $r= \cos (\frac{15}{16}\theta)$ when the domain grows bigger and bigger.

Question

Graph $r= \cos (\frac{15}{16}\theta)$, what pattern of the graph we will get and explain what happen if the domain grows bigger?

Answer 1

This is from $0$ to $\pi$:

Note that the ends don't connect.

This is from $0$ to $2\pi$:

$0$ to $8\pi$:

And it starts repeating after $32\pi$: