Question

a rotating beacon is located at point a next to a long wall. (see the figure to the right.) the beacon is 4 m from the wall. the distance a is given by a = 4|sec 2πt|, where t is time measured in seconds since the beacon started rotating (when t = 0, the beacon is aimed at point r.) find a for t = 0.63. a ≈ meters (type an integer or decimal rounded to one decimal place as needed.)

Explanation:

Step1: Recall secant function definition

$\sec x=\frac{1}{\cos x}$, so $a = 4|\sec(2\pi t)|=\frac{4}{|\cos(2\pi t)|}$.

Step2: Substitute $t = 0.63$

First, calculate $2\pi t$ when $t = 0.63$. So $2\pi\times0.63=1.26\pi$. Then find $\cos(1.26\pi)$.
$\cos(1.26\pi)\approx - 0.79$.

Step3: Calculate the value of $a$

$a=\frac{4}{|\cos(1.26\pi)|}=\frac{4}{| - 0.79|}\approx5.1$.

Answer:

$5.1$