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

[laura11]

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.

 

[Office_Shredder]

What have you tried so far? Do you know what a general sinusoidal function is going to look like in equation form?

 

[laura11]

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

 

[laura11]

the phase shift is what I am really having trouble with

 

[Office_Shredder]

It says the average height of the tide is 3 meters. $$2 \sin(\frac{\pi}{6}x)$$ 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?

 

[laura11]

would you shift it up 3?

 

[laura11]

is the answer y=2sin(pi/6x) +3?

 

[laura11]

yesss.. nooo?? haha

 

[Office_Shredder]

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?