Modeling/Solving Trigonometric Equation

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Modeling/Solving Trigonometric Equation

Given: y = A cos(Bx − C) + D. The depth of water at the end of a pier varies with the tides. High tide = 4 a.m. w/ a depth of 6 meters. Low tide = 10 a.m. w/ a depth of 2 meters. 

A. Model the problem by using the given trigonometric equation to show the depth of the water t hours after midnight, showing all your work.

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

C. A large boat needs at least 4 meters of water to secure it at the end of the pier. Determine what span of time after noon, including both a starting and ending time, the boat can first safely be secured, justifying your answer.