Answer
$$\eqalign{
& {\text{amplitude: }}3 \cr
& {\text{period: }}2\pi \cr
& {\text{vertical translation}}:{\text{none}} \cr
& {\text{phase shift}}:\frac{\pi }{2}{\text{ to the left}} \cr} $$
Work Step by Step
$$\eqalign{
& y = 3\cos \left( {x + \frac{\pi }{2}} \right) \cr
& {\text{Rewrite the function}} \cr
& y = 3\left[ {\cos \left( {x - \left( { - \frac{\pi }{2}} \right)} \right)} \right] + 0 \cr
& {\text{The function is written in the form }}y = a\cos \left[ {b\left( {x - d} \right)} \right] + c \cr
& \underbrace {y = 3\left[ {\cos \left( {x - \left( { - \frac{\pi }{2}} \right)} \right)} \right] + 0}_{y = a\cos \left[ {b\left( {x - d} \right)} \right] + c} \cr
& {\text{with:}} \cr
& a = 3,\,\,\,b = 1,\,\,\,\,d = - \frac{\pi }{2},{\text{ }}c = 0 \cr
& \cr
& {\text{The amplitude is given by }}\left| a \right|,\,\,\,\,\left| a \right| = \left| 3 \right| = 3 \cr
& {\text{The period is given by }}\frac{{2\pi }}{b} = \frac{{2\pi }}{1} = 2\pi \cr
& {\text{The vertical translation is }}c = 0,{\text{ none}} \cr
& {\text{The phase shift is }}d{\text{ translation is }}\left| d \right| = \frac{\pi }{2}{\text{ }}\left( {{\text{ }}d < 0{\text{ to the left}}} \right) \cr
& \cr
& {\text{amplitude: }}3 \cr
& {\text{period: }}2\pi \cr
& {\text{vertical translation}}:{\text{none}} \cr
& {\text{phase shift}}:\frac{\pi }{2}{\text{ to the left}} \cr} $$
