#### Answer

Period$=\frac{\pi}{5}$ seconds
Frequency=$\frac{5}{\pi}$ cycles per second

#### Work Step by Step

The period can be found by first comparing the equation $s(t)=-4\cos 10 t$ to $s(t)=a\cos w t$ to find $w$ which is the angular velocity.
By comparing the two equations, we find that $w=10$. Next, we find the period using the formula:
Period$=\frac{2\pi}{w}$
Period$=\frac{2\pi}{10}$
Period$=\frac{\pi}{5}$ seconds.
Since frequency is the reciprocal of the period, the frequency is $\frac{5}{\pi}$ cycles per second.