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Chapter 4: Problem 56
Find (if possible) the complement and supplement of each angle. (a) \(130^{\circ}\) (b) \(170^{\circ}\)
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Use a graphing utility to graph the function. Describe the behavior of the function as \(x\) approaches zero. $$ y=\frac{6}{x}+\cos x, \quad x>0 $$
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 \()\) $$ f(x)=\tan x $$
Sketch the graph of the function. Include two full periods. $$ y=-\frac{1}{2} \tan x $$
Use a graphing utility to graph \(f, g\), and \(y=x\) in the same viewing window to verify geometrically that \(g\) is the inverse function of \(f\). (Be sure to restrict the domain of \(f\) properly.) $$ f(x)=\sin x, \quad g(x)=\arcsin x $$
Use a calculator to evaluate the expression. Round your result to two decimal places. $$ \arcsin 0.65 $$
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