Answer
$4$ seconds
Work Step by Step
From sine function of $y=a\sin (bx-c)$ and for the given function $v=1.75\sin (\pi t/2)$, $b=\frac{\pi}{2}$.
Then,
$$period=\frac{2\pi}{b}=\frac{2\pi}{\frac{\pi}{2}}=4$$
Thus, the time for one full respiratory cycle is $4$ seconds.
