Solve Tide Depth Model with Trig Functions: A, B, C, and D Variables Explained

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Paulo2014
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Homework Statement


The depth, d, of the tide in a bay is modeled by the formula
d=A+Bcos(Ct+D) where A,B,C and D are constants, d is measured in metres and t in hours.

The time between successive high tides is 14 hours. The maximum depth of the tide in the bay is 5 m and the minimum depth is 1m. Initially the depth is 4m and the tide is coming in

Find A,B,C and D


How do I do this?
 

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Paulo2014 said:
The maximum depth of the tide in the bay is 5 m and the minimum depth is 1m.

For the function d=A+Bcos(Ct+D), when d=5, the function is maximum, are you able to find an equation in A and B only from this?

(Hint: cos(t) has a maximum of 1 regardless of t, thus for cos(Ct+d), will have a maximum of ?)

Similarly for d=1, it has a minimum value.