Answer
$6$ seconds per cycle
Work Step by Step
From sine function $y=a\sin b(x-c)$ and for function $v=0.85\sin (\pi t/3)$, $b=\frac{\pi}{3}$.
$$Period=\frac{2\pi}{b}=\frac{2\pi}{\frac{\pi}{3}}=6$$
Thus, the time for one full respiratory cycle is $6$ seconds per cycle.
