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Math Help - Graphing and finding trig function with given data

  1. #1
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    Graphing and finding trig function with given data

    Another trig question i'm not getting right is the following:

    "A population of animals oscillates sinusoidally between a low of 300 on January 1 and a high of 1200 on July 1. Graph the population against time and use your graph to find a formula for the population P as a function of time t, in months since the start of the year. Assume that the period of P is one year."

    From that, I plugged in the following variables to the formula f(t) = Asin(B(t+h))+C

    A = ((1200-300)/2) = 450
    period = 12m --> 2π/B = 12, B = π/6
    h (right horizontal shift) = -3
    c (upwards vertical shift) = 750

    and I got

    f(t) = 450sin( π/6(t-3)+750

    which looks fine on my calculator, but is wrong according to my h/w. I can't seem to find where I messed up, or of I am missing something entirely.

    Any help is greatly appreciated.
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  2. #2
    MHF Contributor
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    Re: Graphing and finding trig function with given data

    Hey rodryk.

    In your problem, does January first correspond to x = 0? If so your value should be -3*pi/2 radians.
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