#### Answer

Refer to the graph below.

#### Work Step by Step

The given equation is already in the form $y=c+a\cdot \sin{[b(x-d)]}$.
Find one interval of the given function whose length is one period:
\begin{array}{ccccc}
&0 &\le &x+\frac{\pi}{2}&\le &2\pi
\\&0-\frac{\pi}{2} &\le &x+\frac{\pi}{2}-\frac{\pi}{2} &\le &2\pi-\frac{\pi}{2}
\\&-\frac{\pi}{2} &\le &x &\le &\frac{3\pi}{2}
\end{array}
Thus, one interval of the given function is $[-\frac{\pi}{2}, \frac{3\pi}{2}]$.
Dividing this interval into four equal parts yield the key x-values $-\frac{\pi}{2}, 0, \frac{\pi}{2}, \pi,$ and $\frac{3\pi}{2}$.
To graph the given function, perform the following steps:
(1) Create a table of values for the function $y=-3+2\sin{\left(x+\frac{\pi}{2}\right)}$ 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.)