| Answer: The easiest way to begin is to graph the
known data. For graphing the cosine function use the
normal 4 variable form:
y =A + B cos (C (x – D))
To find the amplitude, take the difference between
the maximum and minimum height and divide by 2. This
is because the amplitude is the distance from the highest
point to the middle, and the middle to the lowest point.
A= ½ [maximum height- minimum height]
A= ½ [4.4-1.8]
A=1.3
Because a cosine curve completes half a cycle between
the highest and lowest point.
Period = 2[time of min depth – time of max depth]
Period = 2[14-8]
Period = 2[6]
Period = 12
This implies that C=2?/p˜0.524. High tide occurs
at 8 AM, thus the left endpoint can be considered D/C=4.
So the D value is approximately 2.094. Also, because
the average depth of the water is ½[4.4=1.8]
the A value equals 3.1.
Thus the cosine function for this problem is:
Y=3.1+1.3cos(0.524(x-2.094))
Because the sine curve uses most of the same data,
it looks like:
Y=3.1+1.3sin(.0524(x-0.524))
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