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Chapter 4: Problem 5
Evaluate the expression without using a calculator. $$\arcsin \frac{1}{2}$$
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Fill in the blank. If not possible, state the reason. $$\text { As } x \rightarrow-\infty, \text { the value of } \arctan x \rightarrow\text { _____ } .$$
A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above sea level?
Use a graphing utility to graph the function. $$f(x)=\pi-\sin ^{-1}\left(\frac{2}{3}\right)$$
Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\sin x-\cos \left(x+\frac{\pi}{2}\right), \quad g(x)=2 \sin x$$
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. $$f(x)=e^{-x} \cos x$$
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