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Chapter 4: Problem 54
determine whether the statement is true or false. Justify your answer. $$\cos \left(-\frac{7 \pi}{2}\right)=\cos \left(\pi+\frac{\pi}{2}\right)$$
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Area of a Sector of a Circle Find the area of the sector of a circle of radius \(r\) and central angle \(\boldsymbol{\theta}\). $$r=12 \text { millimeters, } \theta=\frac{\pi}{4}$$
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 \(y=\sin x\)
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. Use the graph to determine the behavior of the function as \(x \rightarrow c\). (a) As \(x \rightarrow 0^{+},\) the value of \(f(x) \rightarrow\) (b) As \(x \rightarrow 0^{-},\) the value of \(f(x) \rightarrow\) (c) As \(x \rightarrow \pi^{+},\) the value of \(f(x) \rightarrow\) (d) As \(x \rightarrow \pi^{-},\) the value of \(f(x) \rightarrow\) $$f(x)=\csc x$$
Finding Arc Length Find the length of the are on a circle of radius \(r\) intercepted by a central angle \(\boldsymbol{\theta}\). $$r=3 \text { meters, } \theta=150^{\circ}$$
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