Solving a trigonometric equation modeling a real-world situati ? Suppose that an

Question

Solving a trigonometric equation modeling a real-world situati ? Suppose that an airplane is asked to stay in a holding pattern near an airport. The distance of the plane to the airport is described by the following. 2z d(r) = 141+66sin( t In this equation, d () is the distance of the plane to the alirport (in miles), and t is the time (in minutes) after the plane enters the holding pattern During the first 12 minutes after the plane enters the holding pattern, when will the plane be 180 miles from the airport? Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a minute. (If there is more than one answer, enter additional answers with the "or" button.) t-minutes Check

Explanation / Answer

d(t) = 141 + 66 sin ( 2pi / 12 t )

plugging d (t) = 180

180 = 141 + 66 sin ( 2pi / 12 t )

180 - 141 = 66 sin ( 2pi / 12 t )

39 / 66 = sin ( 2pi / 12 t )

0.59 = sin ( 2pi/12 t )

2pi/12 t = sin^-1 ( 0.59 )

t = 1.21 minutes

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