1. On February 10, 1990, high tide in Boston was at midnight. The water level at high tide was 9.9 feet; later, at low tide, it was 0.1 feet. Assuming the next high tide is at exactly 12 noon and that the height of the water is given by a sine or cosine curve, find a formula for the water level in Boston as a function of time, measured in hours since midnight.
2. Of course, there's something wrong with the assumption in the problem above that the next high tide is exactly at noon. If so, the high tide would always be at noon or midnight, instead of progressing slowly through the day, as in fact it does. The interval between successive high tides actually averages about 12 hours 24 minutes. Using this, give a more accurate formula for the height of the water as a function of time.
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4 comments:
how do you find what you multiple the input by in the function? i know it has something to do with the period, but i forgot what you divide.
Virginia, you divide 2pie by the period. For number 1, I think the period is 12 hours. So I didvided 2pie by 12 to find the number to multiply to input. Does this help?
For number 2, would the only thing that changes be the period? like the equilibrium position would stay the same, right?
I think so, Michael.
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