# Thread: Math Modelling with Periodic Functions

1. ## 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.

2. ## Re: Math Modelling with Periodic Functions

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

$\displaystyle y = A\sin(Bx+C)+D$

amplitude, $\displaystyle A = 2$ was given.

horizontal distance between consecutive max/min turning points is $\displaystyle 2\pi$ units ... this is the period, $\displaystyle T$ , of the function.

note for future reference, $\displaystyle B = \frac{2\pi}{T}$ for both sine and cosine functions.

horizontal midline between the max and min values is $\displaystyle y = 2 \implies D = 2$

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

$\displaystyle y = 2\sin(x + C) + 2$

how can you determine $\displaystyle C$ ?