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Chapter 4: Problem 20
The sun is \(20^{\circ}\) above the horizon. Find the length of a shadow cast by a park statue that is 12 feet tall.
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Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \tan x=1 $$
Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\). (a) \(x \rightarrow \frac{\pi^{+}}{2}\left(\right.\) as \(x\) approaches \(\frac{\pi}{2}\) from the right (b) \(x \rightarrow \frac{\pi^{-}}{2}\left(\right.\) as \(x\) approaches \(\frac{\pi}{2}\) from the left (c) \(x \rightarrow-\frac{\pi^{+}}{2}\left(\right.\) as \(x\) approaches \(-\frac{\pi}{2}\) from the right \()\) (d) \(x \rightarrow-\frac{\pi^{-}}{2}\left(\right.\) as \(x\) approaches \(-\frac{\pi}{2}\) from the left \()\) $$ f(x)=\tan x $$
PATTERN RECOGNITION (a) Use a graphing utility to graph each function. $$ \begin{array}{l} y_{1}=\frac{4}{\pi}\left(\sin \pi x+\frac{1}{3} \sin 3 \pi x\right) \\ y_{2}=\frac{4}{\pi}\left(\sin \pi x+\frac{1}{3} \sin 3 \pi x+\frac{1}{5} \sin 5 \pi x\right) \end{array} $$ (b) Identify the pattern started in part (a) and find a function \(y_{3}\) that continues the pattern one more term. Use a graphing utility to graph \(y_{3}\) (c) The graphs in parts (a) and (b) approximate the periodic function in the figure. Find a function \(y_{4}\) that is a better approximation.
Sketch the graph of the function. Include two full periods. $$ y=\frac{1}{2} \sec \pi x $$
Use a graph to solve the equation on the interval \([-2 \pi, 2 \pi]\). $$ \csc x=-\frac{2 \sqrt{3}}{3} $$
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