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March 25, 2017

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On a typical day at an ocean port, the water has a maximum depth of 18m at 6:00 am. The minimum depth of 9m occurs 6.8 hours later. Write an equation to describe the relationship between the depth and time.

  • trig - ,

    the period is 2*6.8 = 13.6, so we have

    d(t) = a*cos(2pi/13.6 t) = a*cos(.462t)

    The max-min range is 18-9 = 9, so the amplitude is 4.5 and we have

    d(t) = 4.5 cos(.462t)

    If we call t is the hour of the day, then max is at t=6, so

    d(t) = 4.5 cos(.462(t-6))

    Since the average depth is (9+18)/2, we have

    d(t) = 4.5 cos(.462(t-6)) + 13.5

    To see the graph, visit

    http://rechneronline.de/function-graphs/

    enter the function as

    4.5 cos(.462*(x-6))+13.5

    and set the x-range at 0-20
    the y-range at 0-20

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