What is the Starting Time for Modeling Tide Motion Using a Sine Function?

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In summary, the tide in a local coastal community can be modeled using a sine function with a period of 12 hours and an amplitude of 2. To shift the function up to an average height of 3 meters, the vertical shift would be 3. The phase shift can be determined by choosing a time for x=0, which would correspond to the time when the tide is at its average height of 3 meters. The final equation for the tide motion would be y=2sin(pi/6x) +3.
  • #1
laura11
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The tide in a local costal community can be modeled using a sine function. Starting at noon, the tide is at its "average" height of 3 metres measured on a pole located off of the shore. 5 hours later is high tide with the tide at a height of 5 metres measured at the same pole. 15 hours after noon is low tide with the tide at a height of 1 metre measured at the same pole. Use this information to model the tide motion using a sine function. Show all work.
 
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  • #2
What have you tried so far? Do you know what a general sinusoidal function is going to look like in equation form?
 
  • #3
i know the period is 12 hours which will be pi/6 in the equation
im pretty sure the amplitude is 2
so i know its going to be something like y=2sin(pi/6x)
but thn i don't know the vertical shift or horizontal shift
 
  • #4
the phase shift is what I am really having trouble with
 
  • #5
It says the average height of the tide is 3 meters. [tex]2 \sin(\frac{\pi}{6}x)[/tex] has an average height of 0 (it oscillates between -2 and 2). How much do you have to shift it up to get an average height of 3?

For the phase shift, what time is x=0 going to correspond to?
 
  • #6
would you shift it up 3?
 
  • #7
is the answer y=2sin(pi/6x) +3?
 
  • #8
yesss.. nooo?? haha
 
  • #9
That could be right. The problem doesn't specify what time x=0 is at. So you get to pick. What time does x=0 represent?
 

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