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Chapter 4: Problem 10
Find the period and amplitude. $$y=\frac{3}{2} \cos \frac{\pi x}{2}$$
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Use a graphing utility to graph the function. Use the graph to determine the behavior of the function as \(x \rightarrow c\) (a) \(x \rightarrow\left(\frac{\pi}{2}\right)^{+}\) (b) \(x \rightarrow\left(\frac{\pi}{2}\right)^{-}\) (c) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{+}\) (d) \(x \rightarrow\left(-\frac{\pi}{2}\right)^{-}\) $$f(x)=\tan x$$
Finding Arc Length Find the length of the are on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). $$r=15 \text { inches, } \theta=120^{\circ}$$
Use a graphing utility to graph the function. $$f(x)=\frac{\pi}{2}+\cos ^{-1}\left(\frac{1}{\pi}\right)$$
Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\cos ^{2} \frac{\pi x}{2}, \quad g(x)=\frac{1}{2}(1+\cos \pi x)$$
Determine whether the statement is true or false. Justify your answer. You can obtain the graph of \(y=\sec x\) on a calculator by graphing a translation of the reciprocal of \(y=\sin x\)
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