$r = \sin(3\theta)$ Manual graph

Question

What is the thought process behind the second line of the following, namely that the sin of 3 theta equals +/- 1? Thank you.

$r = \sin(3\theta)$

$\sin3\theta = +- 1$

$3\theta = (2k+1)\frac{\pi}{2}$

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Answer 1

I suspect it means $-1\leq3\theta\leq1$.

The other likelihood is that there's some other part we're not seeing which prevents $\sin(3\theta)$ taking the non-unitary values, thereby enabling the deduction that $\sin(3\theta)=-1$ or $\sin(3\theta)=1$.