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Chapter 4: Problem 49
Find the exact value of each trigonometric function. Do not use a calculator. $$\sin \left(-\frac{\pi}{4}-1000 \pi\right)$$
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Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. $$y=-4 \cos \left(2 x-\frac{\pi}{2}\right)$$
Use a graphing utility to graph $$ y=\sin x+\frac{\sin 2 x}{2}+\frac{\sin 3 x}{3}+\frac{\sin 4 x}{4} $$ in a \(\left[-2 \pi, 2 \pi, \frac{\pi}{2}\right]\) by [-2,2,1] viewing rectangle. How do these waves compare to the smooth rolling waves of the basic sine curve?
Determine whether each statement makes sense or does not make sense, and explain your reasoning. When an angle's measure is given in terms of \(\pi,\) I know that it's measured using radians.
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. $$y=-3.5 \cos \left(\pi x-\frac{\pi}{6}\right) \text { and } y=-3.5 \sec \left(\pi x-\frac{\pi}{6}\right)$$
The average monthly temperature, \(y,\) in degrees Fahrenheit, for Juneau, Alaska, can be modeled by \(y=16 \sin \left(\frac{\pi}{6} x-\frac{2 \pi}{3}\right)+40,\) where \(x\) is the month of the year \(\quad\) (January \(=1,\) February \(=2, \ldots\) December \(=12\) ). Graph the function for \(1 \leq x \leq 12 .\) What is the highest average monthly temperature? In which month does this occur?
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