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Math Help - phase shift

  1. #1
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    phase shift

    A ferris wheel has a diametre of 50.5 metre and takes 2 min to complete a rotation. The lowest point is 2.5 metres from the ground.

    I need to write an equation to represent the graph. So far I have y=25.25sin(3x-b)+27.75.

    How do I calcualte the phase shift? Is my equation completely off?

    Thanks,
    Christine
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  2. #2
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    If you had a sine graph of the form \displaystyle y = a\sin{(bx - c)} + d,

    Your amplitude \displaystyle a = 25.25 is correct.

    Your vertical translation \displaystyle d = 27.75 is correct.

    Your calculation of \displaystyle b is incorrect.

    The period is \displaystyle 2, so you should have \displaystyle 2 = \frac{2\pi}{b}

    \displaystyle b = \frac{2\pi}{2} = \pi.


    So you should have \displaystyle y = 25.25\sin{(\pi x - c)} + 27.75.


    To evaluate the phase shift, you need a coordinate on the graph. Do you know the height when the ferris wheel starts?
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  3. #3
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    The ferris wheel is 2.5metres above the ground.
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  4. #4
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    how did u determine the period is 2?
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  5. #5
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    Because it says it takes 2 mins to complete a rotation.

    And I know it's 2.5m above the ground. I'm asking, what is the height of the basket when it starts? It's the height of one particular basket that is being graphed...
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  6. #6
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    oh... no it does not... your help is greatly appreciated!
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  7. #7
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    Then I expect you can assume it starts at the bottom, where the height is 2.5m.

    So you have a point \displaystyle (x, y) = (0, 2.5).

    Substitute this into your equation and you can solve for \displaystyle c.
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