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Chapter 4: Problem 76
In Exercises \(61-86,\) use reference angles to find the exact value of each expression. Do not use a calculator. $$\tan \left(-\frac{\pi}{6}\right)$$
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Will help you prepare for the material covered in the next section. a. Graph \(y=\sin x\) for \(-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\) b. Based on your graph in part (a), does \(y=\sin x\) have an inverse function if the domain is restricted to \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] ?\) Explain your answer. c. Determine the angle in the interval \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\) whose sine is \(-\frac{1}{2} .\) Identify this information as a point on your graph in part (a).
Have you ever noticed that we use the vocabulary of angles in everyday speech? Here is an example: My opinion about art museums took a \(180^{\circ}\) turn after visiting the San Francisco Museum of Modern Art. Explain what this means. Then give another example of the vocabulary of angles in everyday use.
Carbon dioxide particles in our atmosphere trap heat and raise the planet's temperature. Even if all greenhousegas emissions miraculously ended today, the planet would continue to warm through the rest of the century because of the amount of carbon we have already added to the atmosphere. Carbon dioxide accounts for about half of global warming. The function $$y=2.5 \sin 2 \pi x+0.0216 x^{2}+0.654 x+316$$ models carbon dioxide concentration, \(y,\) in parts per million, where \(x=0\) represents January \(1960 ; x=\frac{1}{12},\) February \(1960 ; x=\frac{2}{12},\) March \(1960 ; \ldots, x=1,\) January \(1961 ; x=\frac{13}{12}\) February \(1961 ;\) and so on. Use a graphing utility to graph the function in a [30,48,5] by [310,420,5] viewing rectangle. Describe what the graph reveals about carbon dioxide concentration from 1990 through 2008
Use a vertical shift to graph one period of the function. $$y=\cos x+3$$
Use a graphing utility to graph each function. Use a viewing rectangle that shows the graph for at least two periods. $$y=\frac{1}{2} \tan \pi x$$
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