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Chapter 4: Problem 40
Determine the amplitude and period of each function. Then graph one period of the function. $$y=-3 \cos \frac{1}{3} x$$
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Graph \(f, g,\) and \(h\) in the same rectangular coordinate system for \(0 \leq x \leq 2 \pi .\) Obtain the graph of h by adding or subtracting the corresponding \(y\) -coordinates on the graphs of \(f\) and \(g\) $$f(x)=2 \cos x, g(x)=\cos 2 x, h(x)=(f+g)(x)$$
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 vertical shift to graph one period of the function. $$y=\sin x-2$$
Use the keys on your calculator or graphing utility for converting an angle in degrees, minutes, and seconds \(\left(D^{\circ} M^{\prime} S^{\prime \prime}\right)\) into decimal form, and vice versa. Convert each angle to \(D^{\circ} M^{\prime} S^{\prime \prime}\) form. Round your answer to the nearest second. $$50.42^{\circ}$$
Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot 2 x$$
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