Answer
The graph of $r=θ~sin~θ,~~-6\pi\leq θ\leq6\pi$
Work Step by Step
$y=sin~x$ is a periodic function. The domain required for an entire period is $2\pi$, that is, $0\leq x\leq2\pi$
$r=θ~sin~θ$
Domain required for an entire period of $sin~θ$:
$0\leq θ\leq2\pi$
But, notice that $r=θ~sin~θ$ is not a periodic function because $θ$ is not periodic. Compare $r=θ~sin~θ$ (above) with $r=sin~θ$ (below). The last equation is a circumference of radius $0.5$ with center at $(0,0.5)$.
