Question 1209251
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Let w = sin(pi*t/20​)


45sin(pi*t/20​) + 50 becomes 45w + 50


Solving 45w + 50 = 72.5 leads to w = 0.5 and it leads back to sin(pi*t/20​) = 0.5


If sin(x) = 0.5 in radian mode, then x = pi/6 and x = 5pi/6 are two possibilities when considering the interval {{{0 <= x < 2pi}}}
This is something to memorize since it comes up a lot in trig. Alternatives are to use a reference sheet, unit circle, or a calculator.
We use the smaller of those x values since we're interested when the passenger reaches 72.5 meters the first time. If we changed "first time" to "second time", then we'd use 5pi/6 instead.


So,
sin(pi*t/20​) = 0.5
sin(pi*t/20​) = sin(pi/6)
pi*t/20​ = pi/6
t/20​ = 1/6
t = (1/6)*20
t = 20/6
t = 10/3
t = 3.3333... where the '3's go on forever
This is the number of minutes it takes to arrive at the first instance of being 72.5 meters above the ground.
Round that decimal value however your teacher instructs.
Or you can stick with the fraction form.



Extra info:
(10/3) minutes = (10/3)*60 = 200 seconds
200 seconds = 180 seconds + 20 seconds = 3 minutes + 20 seconds
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