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Math Help - Find a Trigonometric equation

  1. #1
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    Find a Trigonometric equation

    Give an equation for a cosine funtion that has a maximum at (pi/4, 8), followed immediately by another maximum at (9pi/4,8), and has a minimum at value of 4.

    This is what I did

    Amplitude = (8-4)/2
    = 2

    Vertical shift = 8-2 =6

    So far I got this
    y = 2cos (x -? )+6

    How do I find the phase shift
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  2. #2
    MHF Contributor
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    The cosine function normally has consecutive maximums at x = 0 and x = 2\pi. Your function has consecutive maximums at x = \frac{\pi}{4} and x = \frac{9\pi}{4}. This means the period is \frac{9\pi}{4} - \frac{\pi}{4} = 2\pi, which is normal for the cosine function. So what is the phase shift when you move (0, 8) to (\frac{\pi}{4}, 8)?
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