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Math Help - trigonometric graph

  1. #1
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    Question trigonometric graph

    1. The curve above is the graph of a sinusoidal function. It goes through the point and . Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.



    2.The curve above is the graph of a sinusoidal function. It goes through the points and . Find a sinusoidal function that matches the given graph. If needed, you can enter =3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits.

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  2. #2
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    1. looks like a -sine curve

    amplitude = 3
    period = 6
    phase shift = none
    vertical shift = +3

    y = -3sin\left(\frac{\pi}{3}x\right) + 3

    2. I'd use a cosine curve for this one ...

    amplitude = 4
    period = 6
    phase shift = left 2
    vertical shift = none

    you try it.
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  3. #3
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    changing the sine function

    You need to find a solution of the form

    A + B sin (Cx - D)

    where A shifts the wave up, here A = 3 as the wave moves around +3

    B gives the size up and down, if B = 1 we have a size of 2, so we want B = 3 as we have a size of 6

    C controls the period, a normal wave is period 2 pi, we want period 6, so C = pi/3

    D controls the shift to the right, we actually want the shift to the left so that Cx - D = 0 when x = -3 hence D = -pi
    <br />
y = 3 + 3sin\left(\frac{\pi}{3}x + \pi\right) <br />


    hope this helps you do the second question on your own.

    cheers

    Nobby
    Last edited by Nobby; September 25th 2008 at 04:43 PM. Reason: error
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  4. #4
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    for question 2..i got 4cos(pi/3) but i dont know what to do for phase shift
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  5. #5
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    y = 4\cos\left[\frac{\pi}{3}(x + 2)\right]
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