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Math Help - Application of Cosine Problem

  1. #1
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    Application of Cosine Problem

    The tide, or depth of the ocean near the shore, changes throughout the day. The water depth d (in feet) of a bay can be modeled by

    d = 35-28\cos{\frac {\pi}{6.2}}{t}

    where t is the time in hours, with t=0 corresponding to 12:00 A.M.

    (a) Algebraically find the times at which the high and low tides occur.
    How would I do this? Just solve for d ? Wouldn't I just get one answer? I need two, one for the high and one for the low.

    (b) Algebraically find the time(s) at which the water depth is 3.5 feet.
    Just d for 3.5 and solve right? I have one question though...how would you determine \cos {\frac {\pi}{6.2}} algebraically?

    I have also attached a picture of the original problem.
    Attached Thumbnails Attached Thumbnails Application of Cosine Problem-5-ps-10.bmp  
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  2. #2
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    Quote Originally Posted by chrozer View Post
    The tide, or depth of the ocean near the shore, changes throughout the day. The water depth d (in feet) of a bay can be modeled by

    d = 35-28\cos{\frac {\pi}{6.2}}{t}

    where t is the time in hours, with t=0 corresponding to 12:00 A.M.

    (a) Algebraically find the times at which the high and low tides occur.
    How would I do this? Just solve for d ? Wouldn't I just get one answer? I need two, one for the high and one for the low.

    (b) Algebraically find the time(s) at which the water depth is 3.5 feet.
    Just d for 3.5 and solve right? I have one question though...how would you determine \cos {\frac {\pi}{6.2}} algebraically?

    I have also attached a picture of the original problem.
    -1 \leq \cos(anything) \leq 1

    low tide (d = 7 ft) occurs when \cos\left(\frac{\pi t}{6.2}\right) = 1

    first low tide is when \frac{\pi t}{6.2} = 0


    high tide (d = 63 ft) occurs when \cos\left(\frac{\pi t}{6.2}\right) = -1

    first high tide is when \frac{\pi t}{6.2} = \pi


    part (b) has no solution ... the lowest depth is 7 ft.
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  3. #3
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    Quote Originally Posted by skeeter View Post
    -1 \leq \cos(anything) \leq 1

    low tide (d = 7 ft) occurs when \cos\left(\frac{\pi t}{6.2}\right) = 1

    first low tide is when \frac{\pi t}{6.2} = 0


    high tide (d = 63 ft) occurs when \cos\left(\frac{\pi t}{6.2}\right) = -1

    first high tide is when \frac{\pi t}{6.2} = \pi


    part (b) has no solution ... the lowest depth is 7 ft.
    Ok so I found that the solutions to the low tides is at when t = 0, 12.4, 24.8, and so on.
    So the times are 12:00 A.M., 12:24 P.M. and 12:48 A.M. So low tides occur every 12 hours and 24 minutes from 12:00 A.M. right?

    And the solutions to the high tide is at when t = 6.2, 18.6, 31, and so on.
    So the times are 6:12 A.M., 6:36 P.M. and 7:00 A.M. So high tides occur every 12 hours and 24 minutes from 6:12 A.M. right?
    Last edited by chrozer; February 28th 2009 at 05:07 PM.
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  4. #4
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    correct ...

    period of the cycle, T = \frac{2\pi}{\frac{\pi}{6.2}} = 12.4 hrs
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