Tide and trig

  • Thread starter TonyC
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  • #1
TonyC
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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?
 

Answers and Replies

  • #2
VietDao29
Homework Helper
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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,
 
  • #3
TonyC
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What are you looking for?
 
  • #4
VietDao29
Homework Helper
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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,
 
  • #5
mathmike
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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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