Math Modelling with Periodic Functions

I need help with deriving a periodic function out of the following given information. Question from the book has been provided.

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Question: from the information below, create a periodic function of the form y = Asin(Bx + C) + D and then sketch the curve where 0 ≤ x ≤ 4π

The curve has:

- An amplitude of 2

- Consecutive minimum turning points at: (7π/4, 0) and at (15π/4, 0)

- Consecutive maximum turning points at: (3π/4, 4) and at (11π/4, 4)

Extra Notes

π is the symbol Pi if you can't see it properly.

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Re: Math Modelling with Periodic Functions

first step would be to sketch the described graph so you can visualize what's happening.

amplitude, was given.

horizontal distance between consecutive max/min turning points is units ... this is the period, , of the function.

note for future reference, for both sine and cosine functions.

horizontal midline between the max and min values is

so, now you're at this point ...

how can you determine ?