For a boat to float in a tidal bay, the water must be at least 2.7 meters deep. The depth of the water around the boat, d(t), in meters,
where t is measured in hours since midnight, is d(t) = 5 + 4.6 sin(0.5t).
(a) What is the period of the tides in hours? (Round your answer to three decimal places.)
I think it is 12.566 hrs.
The period is 2pi/B so 2pi/0.5 which equals 12.566
b) If the boat leaves the bay at midday, what is the earliest time it can return before the water becomes too shallow? (Round your answer to the nearest minute.)
I just don't know how to even start solving this question.
I think maybe this is how you do it? Please correct me!
Is it:
2.7 = 5 + 4.6 sin(0.5t)
(subtract 5 from both sides)
-2.3 = 4.6sin(0.5t)
(divide by 4.6 from both sides)
-0.5=sin(0.5t)
arcsin(-0.5) = 0.5t