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Math Help - finding a trig equation from graph

  1. #1
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    finding a trig equation from graph

    I have a graph, the maximum value is 36, the minimum value is 4 and it cycles every 6 hours. So at time = 0 the graph is at 4 on the y axis, then at time 6 it is at 36, 12 it is at 4 hours, and so on. So the points are (0,4), (6,36), (12,4) etc. I have to find the equation for this graph using a transformation of y = sin(x). So far I have y = 32sin(π/9 t) + 4, but everytime i run this on a graphing simulator the results go into the negative values so i am sure it is wrong I'm really stuck here, and it is quite frustrating, can anyone help. thank you.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Maybe this'll help.

    Try to "center" your equation first by assuming that its max and min are equidistant from the x-axis. Like this:

    36-4=32 and if i center,then it s max and min are both 16 units from the x-axis.

    Now i figure out the equation, and then I add to the right side of the equation whatever I must in order to make it shift up the graph.

    Does that help you?
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  3. #3
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    I sorta know what you mean, it was what i was trying to do, but i still get the wrong graph, it is driving me nuts.
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  4. #4
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    your equation has the form

    y = Asin(nt) + C

    where

    A = the amplitude = (max - min)/2 = (36-4)/2 = 16

    B = the period, where B = \frac{2\pi}{n}

    and C = the vertical translation

    If you wave wavelength is 6 then, 6 = \frac{2\pi}{n}

    and n = \frac{\pi}{3}

    I hope that helps some.
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