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

[Paulo2014]

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?

 

[rock.freak667]

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.

 

[Architeuthis Dux]

I would approach this problem by first understanding the variables and their significance in the tide depth model. A represents the average depth of the tide, B represents the amplitude or difference between the maximum and minimum depths, C represents the frequency or number of cycles per unit of time, and D represents the phase shift or starting point of the tide cycle.

To solve for these variables, I would use the given information about the time between high tides, maximum and minimum depths, and initial depth to create a system of equations. From there, I would use trigonometric identities and algebraic manipulation to solve for A, B, C, and D.

Additionally, I would also consider any external factors that could affect the tide depth, such as wind or weather patterns, and incorporate them into the model if necessary.

Once the variables have been determined, I would then use the model to make predictions about future tide depths and compare them to actual data to assess the accuracy of the model. I would also continue to gather data and make adjustments to the model as needed to improve its accuracy.