Solve the problem.
-A rotating beacon is located $6 \mathrm { ft }$ from a wall. If the distance from the beacon to the point on the wall where the $b$ is aimed is given by
$$a = 6 | \sec 2 \pi t | \text {, }$$
where $t$ is in seconds, find a when $t = 0.28$ seconds. Round your answer to the nearest hundredth.
A) $20.72 \mathrm { ft }$
B) $- 32.02 \mathrm { ft }$
C) $32.02 \mathrm { ft }$
D) $9.41 \mathrm { ft }$

Question

Quizplus · Accepted Answer

To find $a$ when $t = 0.28$ seconds, substitute $t = 0.28$ into the given equation: $a = 6 | \sec 2 \pi (0.28) |$. Calculate $2 \pi (0.28)$, find the secant of this value, take the absolute value, and then multiply by 6. The secant function can be calculated as the reciprocal of the cosine function. After performing these calculations, the result is approximately $32.02 \mathrm { ft }$, which corresponds to choice C.

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