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Math Help - Deriving cosine equation from a chart

  1. #1
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    Deriving cosine equation from a chart

    I've been given the following information:

    x = y
    1 = 9.08
    2 = 9.95
    3 = 11.20
    4 = 12.73
    5 = 14.10
    6 = 15.13
    7 = 15.32
    8 = 14.52
    9 = 13.18
    10 = 11.75
    11 = 10.30
    12 = 9.25
    First, I was asked to derive a sine function to model the data, which I got as: Y=3.12sin[pi/6(x-4)]+12.2

    Now, I need to get a cosine function to model it. This is where I'm stuck; the sine curve has one maximum, as does the data, so I was easily able to figure out the phase shift. But a cosine curve has two maximums so I'm having a little trouble figuring out a cosine equation.

    I decided to check the back of the book and see the answer as y=3.11cos[0.51(m-6.71)]+12.14

    At this point, I'm completely lost

    Could anyone point me into the right direction as to how I'd be able to derive a cosine function from the above data?
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  2. #2
    Senior Member
    Joined
    Nov 2010
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    Clarksville, ARk
    Posts
    398
    Quote Originally Posted by youngb11 View Post
    I've been given the following information:



    First, I was asked to derive a sine function to model the data, which I got as: Y=3.12sin[pi/6(x-4)]+12.2

    Now, I need to get a cosine function to model it. This is where I'm stuck; the sine curve has one maximum, as does the data, so I was easily able to figure out the phase shift. But a cosine curve has two maximums so I'm having a little trouble figuring out a cosine equation.

    I decided to check the back of the book and see the answer as y=3.11cos[0.51(m-6.71)]+12.14

    At this point, I'm completely lost

    Could anyone point me into the right direction as to how I'd be able to derive a cosine function from the above data?

    Were you given a method to use? I suspect that the book answer comes from a least-squares fit, while yours comes from inspecting the data.

    To convert you answer to a cosine answer, recognize that you can obtain the graph of
    y=\sin(x) by shifting the graph of y=\cos(x) by \pi/2 units to the right.

    So, y=3.12\sin[(\pi/6)(x-4)]+12.2 is equivalent to y=3.12\cos[(\pi/6)(x-4)-(\pi/2)]+12.2.

    Do some algebra to compare. I'm puzzled by the variable m in the cosine expression the "book" gave.



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