Question

The water depth in a harbor rises and falls over time. The function f(t) = 4.1 sine (StartFraction pi Over 6 EndFraction t minus StartFraction pi over 3 EndFraction) + 19.7 models the water depth, in feet, after t hours.

During the first 24 hours, at what times does the water depth reach a maximum?

Answer 1

Below

Explanation:

f(t) = 4.1 (sin pi/6 t - pi/3) + 19.7 <===will be a maximum when the sin portion is equal to 1

so sin ( pi/6 t - pi/3) = 1 given that sin is equal to one at 0 and pi and 2 pi and 3 pi and 4 pi etc

pi/6 t - pi/3 = 0 or pi , 2 pi, 3 pi , 4 pi

then t = 2 and 8 and 14 and 20 hrs ( every 6 hrs starting with t = 2)