The tide, or depth of the ocean near the shore, changes throughout the day. The water depth d (in feet) of a bay can be modeled by d = 35 - 28 cos π / 6.2 t where t represents the time in hours, with t = 0 corresponding to 12:00 A.M.
(a) Algebraically find the times at which the high and low tides occur.
(b) If possible, algebraically find the time(s) at which the water depth is 3.5 feet.
(c) Use a graphing utility to verify your results from parts (a) and (b).