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Chapter 4: Problem 67
In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\sin \frac{2 \pi}{3}$$
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will help you prepare for the material covered in the next section.
$$\text { Solve: } \quad-\frac{\pi}{2}
Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\cot \frac{x}{2}$$
A clock with an hour hand that is 15 inches long is hanging on a wall. At noon, the distance between the tip of the hour hand and the ceiling is 23 inches. At 3 P.M., the distance is 38 inches; at 6 P.M., 53 inches; at 9 P.M., 38 inches; and at midnight the distance is again 23 inches. If \(y\) represents the distance between the tip of the hour hand and the ceiling \(x\) hours after noon, make a graph that displays the information for \(0 \leq x \leq 24\)
Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=3 \cos (2 \pi x+4 \pi)$$
For \(x>0,\) what effect does \(2^{-x}\) in \(y=2^{-x} \sin x\) have on the graph of \(y=\sin x ?\) What kind of behavior can be modeled by a function such as \(y=2^{-x} \sin x ?\)
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