Question 1058946: Sinusoidal Equation Problem:
During a 12 hour period, the tides in one area of the Bay of Fundy cause the water level to rise to 6m above average sea level and to fall 6m below average sea level. The depth of the water at low tide is 2m as measured against a pier.
a) Suppose the water is at average sea level (rest position) at 0:00 hours (midnight) and the tide is coming in. Draw a graph that show the height of the tide over a 24 hour period. Explain how you obtained the graph.
b) Write the equation of the sine wave that represents the change in the height of the tide.
c) If the water is at average sea level at 03:00 (3am) instead of at midnight and the tide is coming in, write the equation of the sine wave that represents this situation.
What I have:
Min Value = 2
Amplitude = 6
Vertical Displacement/Rest Position = 8 (Min Value + Amplitude or 2 + 6 = 8)
Max Value = 14 (Rest Position + Amplitude or 8 + 6)
Phase shift = 0 (since measuring cycle from y = 0)
Period = 12 (for 12 hours)
simplified equation for b) in form of y = a sin (2Pi/p) (x-d) + c :
y = 6sin (3.14159/6)x + 8
But I'm not confident I'm on the right track here.
Any help with A) B) or C) is much appreciated.
Answer by ikleyn(52809)   (Show Source):
You can put this solution on YOUR website! .
This phrase
"During a 12 hour period, the tides in one area of the Bay of Fundy cause the water level to rise to 6m above average sea level
and to fall 6m below average sea level"
doesn't describe precisely what happens during this 12-hours period.
One can read/understand it as
"During a 12 hour period, the tide in one area of the Bay of Fundy changes water level from 6m above average sea level
to 6m below average sea level"
and then 12 hours is only half of the tide period, while the entire tide period is 24 hours.
So, this problem (or this difference in reading) is not about the Math.
It is about the exact meaning of the text,
which is, unfortunately, not clear enough to make a unique conclusion.
From the math point of view, your formula is correct UNDER THE ASSUMPTION that the period is 12 hours.
If the period is 24 hours, then simply replace 12 by 24 in your formula.
THE SECOND OPINION (and the third, fourth and so on) is desired.
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And one more IMPORTANT NOTE: in your formula for y (y = . . . ) you MUST explain what is "x".
I understand that it is time, but it must be written/pronunciation directly and explicitly: "x is time in hours, counting from the midnight".
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