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Chapter 4: Problem 16
Determine the amplitude and period of each function. Then graph one period of the function. $$y=-\sin \frac{4}{3} x$$
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Use a graphing utility to graph each pair of functions in the same viewing rectangle. Use a viewing rectangle that shows the graphs for at least two periods. $$y=-3.5 \cos \left(\pi x-\frac{\pi}{6}\right) \text { and } y=-3.5 \sec \left(\pi x-\frac{\pi}{6}\right)$$
Rounded to the nearest hour, Los Angeles averages 14 hours of daylight in June, 10 hours in December, and 12 hours in March and September. Let \(x\) represent the number of months after June and let \(y\) represent the number of hours of daylight in month \(x .\) Make a graph that displays the information from June of one year to June of the following year.
In Chapter \(5,\) we will prove the following identities: $$ \begin{aligned} \sin ^{2} x &=\frac{1}{2}-\frac{1}{2} \cos 2 x \\ \cos ^{2} x &=\frac{1}{2}+\frac{1}{2} \cos 2 x \end{aligned} $$ Use these identities to solve. Use the identity for \(\cos ^{2} x\) to graph one period of \(y=\cos ^{2} x\)
The following figure shows the depth of water at the end of a boat dock. The depth is 6 feet at low tide and 12 feet at high tide. On a certain day, low tide occurs at 6 A.M. and high tide at noon. If \(y\) represents the depth of the water \(x\) hours after midnight, use a cosine function of the form \(y=A \cos B x+D\) to model the water's depth.
Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot \frac{x}{2}$$
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