#### Answer

Refer to the graph below.

#### Work Step by Step

The given equation is already in the form $y=c+a\cdot \cos{[b(x-d)]}$.
Find one interval of the given function whose length is one period:
\begin{array}{ccccc}
&0 &\le &3\left(x-\frac{\pi}{6}\right)&\le &2\pi
\\&\frac{0}{3}&\le &\frac{3\left(x-\frac{\pi}{6}\right)}{3} &\le &\frac{2\pi}{3}
\\&0 &\le &x-\frac{\pi}{6} &\le &\frac{2\pi}{3}
\\&0+\frac{\pi}{6} &\le &x-\frac{\pi}{6}+\frac{\pi}{6} &\le &\frac{2\pi}{3}+\frac{\pi}{6}
\\&\frac{\pi}{6} &\le &x &\le &\frac{5\pi}{6}
\end{array}
Thus, one interval of the given function is $[\frac{\pi}{6}, \frac{5\pi}{6}]$.
Dividing this interval into four equal parts yield the key x-values $\frac{\pi}{6}, \frac{\pi}{3}, \frac{\pi}{2}, \frac{2\pi}{3}, $ and $\frac{5\pi}{6}$.
To graph the given function, perform the following steps:
(1) Create a table of values for the function $y=-\frac{5}{2}+\cos{\left(3(x-\frac{\pi}{6})\right)}$ using the key x-values listed above.
(Refer to the table below.)
(2) Plot each point in the table then connect them using a sinusoidal curve.
(Refer to the attached graph in the answer part above.)