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Tide and trig

  1. Aug 18, 2005 #1
    Suppose the depth of the tide in a certain harbor can be modeled by y=21-5cos pi t/6, whre y is the water depth in feet and t is the time in hours. Consider a day in which t=0 represents 12:00 midnight. For that day, when are the first high tide and the first low tide and what is the water depth at each time?
     
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  3. Aug 18, 2005 #2

    VietDao29

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    You have:
    [tex]-1 \leq \cos \alpha \leq 1[/tex]
    So what can you say about the [tex]y = 21 - 5 \cos \frac{\pi t}{6}[/tex]
    Viet Dao,
     
  4. Aug 18, 2005 #3
    What are you looking for?
     
  5. Aug 18, 2005 #4

    VietDao29

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    Okay, when y is minimum, that means:
    [tex] 5 \cos \frac{\pi t}{6}[/tex] is maximum.
    So [tex] \cos \frac{\pi t}{6}[/tex] is maximum.
    So y is minimum means that [tex] \cos \frac{\pi t}{6}[/tex] is maximum.
    [tex]-1 \leq \cos \frac{\pi t}{6} \leq 1[/tex] so what t makes [tex] \cos \frac{\pi t}{6}[/tex] maximum?
    Viet Dao,
     
  6. Aug 18, 2005 #5
    you can take the first derivitive and then find when it is 0 to tell you where your critical points are then use that to find the min and max
     
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