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Chapter 4: Problem 28
Use a calculator to evaluate the expression. Round your result to two decimal places. $$\cos ^{-1} 0.26$$
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Sketch a graph of the function. $$y=2 \arccos x$$
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. $$h(x)=2^{-x^{2} / 4} \sin x$$
A buoy oscillates in simple harmonic motion as waves go past. The buoy moves a total of 3.5 feet from its low point to its high point (see figure), and it returns to its high point every 10 seconds. Write an equation that describes the motion of the buoy where the high point corresponds to the time \(t=0\) (figure cannot copy)
Determine whether the statement is true or false. Justify your answer. $$\tan \frac{5 \pi}{4}=1 \quad \rightarrow \quad \arctan 1=\frac{5 \pi}{4}$$
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 \(f(x) \rightarrow\) $$f(x)=\csc x$$
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