SOLUTION: Use a cosine function to describe the height of the tides of the ocean if high tide raises the water level to 5 m at noon and low tide drops it down to 1 m at 4 p.m. Let t = 0 be 1
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Question 1205129: Use a cosine function to describe the height of the tides of the ocean if high tide raises the water level to 5 m at noon and low tide drops it down to 1 m at 4 p.m. Let t = 0 be 12 noon. Answer by ikleyn(52884) (Show Source):
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Use a cosine function to describe the height of the tides of the ocean if high tide raises
the water level to 5 m at noon and low tide drops it down to 1 m at 4 p.m. Let t = 0 be 12 noon.
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Mid-line is half the sum of the maximum and the minimum height = = 3 meters.
The amplitude is half the difference of the maximum and the minimum height = = 2 meters.
Since the cosine function has the maximum at 12 noon, which corresponds to t= 0, it means
that the shift of the cosine function is zero.
The half of the period of the cosine function is 4 hours from 12 noon (maximum height)
to 4 p.m. (minimum height) - so, the period is 8 hours.
Now we have everything to write the cosine function for the water level
h(t) = + 3 meters.
