Answer
$t=6k+1\ sec$ and $t=6k+5\ sec$
Work Step by Step
Step 1. Given the model function $d=-4\ cos(\frac{\pi}{3}t)$, at $d=-2\ in$, we have $-4\ cos(\frac{\pi}{3}t)=-2$ or $cos(\frac{\pi}{3}t)=0.5$
Step 2. The general solutions for the above equation are $\frac{\pi}{3}t=2k\pi+\frac{\pi}{3}$ and $\frac{\pi}{3}t=2k\pi+\frac{5\pi}{3}$ or $t=6k+1\ sec$ and $t=6k+5\ sec$, where $k$ is an integer.
