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Chapter 4: Problem 16
Find the period and amplitude. $$y=\frac{5}{2} \cos \frac{x}{4}$$
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Sketch a graph of the function and compare the graph of \(g\) with the graph of \(f(x)=\arcsin x\). $$g(x)=\arcsin (x-1)$$
Write the function in terms of the sine function by using the identity $$A \cos \omega t+B \sin \omega t=\sqrt{A^{2}+B^{2}} \sin \left(\omega t+\arctan \frac{A}{B}\right).$$ Use a graphing utility to graph both forms of the function. What does the graph imply? $$f(t)=3 \cos 2 t+3 \sin 2 t$$
Writing When the radius of a circle increases and the magnitude of a central angle is constant, how does the length of the intercepted arc change? Explain your reasoning.
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?
Find the distance between Dallas, Texas, whose latitude is \(32^{\circ} 47^{\prime} 39^{\prime \prime} \mathrm{N}\) and Omaha, Nebraska, whose latitude is \(41^{\circ} 15^{\prime} 50^{\prime \prime} \mathrm{N}\) Assume that Earth is a sphere of radius 4000 miles and that the cities are on the same longitude (Omaha is due north of Dallas).
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