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Chapter 4: Problem 37
Rewrite each angle in degree measure. (Do not use a calculator.) (a) \(\frac{3 \pi}{2}\) (b) \(\frac{7 \pi}{6}\)
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Consider the functions \(f(x)=\sin x\) and \(f^{-1}(x)=\arcsin x\). (a) Use a graphing utility to graph the composite functions \(f \circ f^{-1}\) and \(f^{-1} \circ f\). (b) Explain why the graphs in part (a) are not the graph of the line \(y=x .\) Why do the graphs of \(f \circ f^{-1}\) and \(f^{-1}\) o \(f\) differ?
Use a graphing utility to graph the function and the damping factor of the function in the same viewing window. Describe the behavior of the function as \(x\) increases without bound. $$f(x)=2^{-x / 4} \cos \pi x$$
Define the inverse cotangent function by restricting the domain of the cotangent function to the interval \((0, \pi),\) and sketch the graph of the inverse trigonometric function.
Sketch a graph of the function. $$f(x)=\arctan 2 x$$
Fill in the blank. If not possible, state the reason. $$\text { As } x \rightarrow \infty, \text { the value of } \arctan x \rightarrow\text { _____ } .$$
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