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Chapter 4: Problem 6
Find the period and amplitude. $$y=3 \cos 2 x$$
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Graph the functions \(f\) and \(g .\) Use the graphs to make a conjecture about the relationship between the functions. $$f(x)=\cos ^{2} \frac{\pi x}{2}, \quad g(x)=\frac{1}{2}(1+\cos \pi x)$$
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 \(f(x) \rightarrow\) $$f(x)=\cot x$$
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?
True or False? Determine whether the statement is true or false. Justify your answer. The difference between the measures of two coterminal angles is always a multiple of \(360^{\circ}\) when expressed in degrees and is always a multiple of \(2 \pi\) radians when expressed in radians.
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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