Recently, I asked for the smallest value of 'a' for which the graph of the curve $r = 5\sin\theta$ is complete. This turned out to be $\pi$ and not $2\pi$, because $\sin(\theta+\pi) = -\sin(\theta)$ (Give the smallest value for 'a' to complete the graph). Now it turns out that the graph of the curve $r = 4\sin2\theta$ is complete for $a = 2\pi$. Now my question is why? I know that $\sin2\theta = 2\sin\theta \cos\theta$, but I still can't relate this property to that. Thanks in advance!