Question

the depth of the ocean and a buoy reaches a maximum of 6 feet and a minimum of 2 feet. the depth d (in feet) of the ocean is modeled by h=2 sin pi/6t + 4 where t is the time (in hours) with t=0 representing 12 a.m.

Answer 1

c.) 5 = 2 sin pi/6 t + 4
2 sin pi/6 t = 5 - 4 = 1
sin pi/6 t = 1/2
pi/6 t = arcsin (1/2) = 2n pi + pi/6, (2n + 1)pi - pi/6 = pi/6(12n + 1), pi/6(12n + 5)
t = 12n + 1, 12n + 5, n = 0, 1, 2, . . .
t = 1, 5

Therefore, the depth is 5 at 1 a.m. and at 5 a.m.