Chapter 4.5, Problem 55E

Prison searchlight. A dual-beam rotating light n a move set is positioned as a spotlight shining on prison wall. The light is 20 feet from the wall and rotates clockwise. The light shines on point P on the wall when first turned on $\left(t=0\right)$. After t seconds, the distance (in feet) from the beam on the wall to the point P is given by the function.

$d\left(t\right)=20\tan \frac{\pi t}{5}$.

When the light beam is to the right of P, the value of d is positive, and when the beam is to the left of P, the value of d is negative.

a. Graph d over the interval $0\le t\le 5$.

b. Since $d\left(t\right)$ is undefined for $t=2.5$, where is the rotating light pointing when $t=2.5$?