# Smallest value of 'a' for which the graph of the curve $r = 4\sin2\theta$ is complete

by Stallmp   Last Updated July 12, 2019 10:20 AM - source

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!

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