Answer
see graph.
Work Step by Step
Given $y=-\frac{5}{2}+cos[3(x-\frac{\pi}{6})]$, we can identify its amplitude as $1$, period as $p=\frac{2\pi}{3}$, vertical translation as $\frac{5}{2}$ down, and phase shift as $\frac{\pi}{6}$ to the right, see graph.
