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Math Help - Math Modelling with Periodic Functions

  1. #1
    Newbie kevi3434's Avatar
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    Post 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.
    '
    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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  2. #2
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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.

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

    amplitude, A = 2 was given.

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

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

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

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

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

    how can you determine C ?
    Attached Thumbnails Attached Thumbnails Math Modelling with Periodic Functions-sinecurve2.jpg  
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