Answer
The amplitude is $\frac{1}{2}$, the period is $\frac{2\pi}{3}$, there is no vertical translation and the phase shift is zero.
Work Step by Step
We first write the equation in the form $y=c+a \cos [b(x-d)]$. Therefore, $y=-\frac{1}{2}\cos (3x)$ becomes $y=0-\frac{1}{2}\cos [3(x-0)]$
Comparing the two equations, $a=-\frac{1}{2},b=3,c=0$ and $d=0$.
The amplitude is $|a|=|-\frac{1}{2}|=\frac{1}{2}.$
The period is $\frac{2\pi}{b}=\frac{2\pi}{3}=\frac{2\pi}{3}$.
The vertical translation is $c=0$.
The phase shift is $|d|=|0|=0$
Therefore, the amplitude is $\frac{1}{2}$, the period is $\frac{2\pi}{3}$, there is no vertical translation and the phase shift is zero.
