Question

Given y=Acos(Bx+C) + D. Throughout the day the depth of water at the end of a pier varies with the tides. High tide occurs at 4 am with a depth of 6 meters. Low tide occurs at 10 am with a depth of 2 meters. Model the problem by using the given trigonometric equation to show the depth of the water t hours after midnight showing all your work.

Solve the problem by finding the depth of the water at noon, explaining, the reasoning.