#### Answer

Frequency$=4$ cycles
Period$=\frac{1}{4}$ sec

#### Work Step by Step

We first write the equation in the form $y=a \cos [b(x-d)]$. Therefore, $y=-4\cos (8\pi t)$ becomes $y=0-4\cos [8\pi(t-0)]$.
Comparing the two equations, $b=8\pi$.
The period can be found from the formula:
$\frac{2\pi}{b}$
Substituting the value of $b$ in this formula and solving:
Period$=\frac{2\pi}{8\pi}$
Period$=\frac{1}{4}$ sec
Since frequency=1/Period,
Frequency$=\frac{1}{1/4}=4$ cycles