91Ó°ÊÓ

An airplane, flying at an altitude of 6 miles, is on a flight path that passes directly over an observer (see figure). If \(\theta\) is the angle of elevation from the observer to the plane, find the distance \(d\) from the observer to the plane when (a) \(\theta=30^{\circ}\), (b) \(\theta=90^{\circ}\), and \((\mathrm{c}) \theta=120^{\circ}\).

Use a graphing utility to graph the function given by \(y=d+a \sin (b x-c),\) for several different values of \(a, b, c,\) and \(d\). Write a paragraph describing the changes in the graph corresponding to changes in each constant.

Find the area of the sector of the circle with radius \(r\) and central angle \(\theta\). $$ \begin{aligned} &2.5 \text { feet }\\\ &225^{\circ} \end{aligned} $$

Assuming that Earth is a sphere of radius 6378 kilometers, what is the difference in the latitudes of Syracuse, New York and Annapolis, Maryland, where Syracuse is about 450 kilometers due north of Annapolis?

The diameter of a DVD is approximately 12 centimeters. The drive motor of the DVD player is controlled to rotate precisely between 200 and 500 revolutions per minute, depending on what track is being read. (a) Find an interval for the angular speed of a DVD as it rotates. (b) Find an interval for the linear speed of a point on the outermost track as the DVD rotates.

A two-inch-diameter pulley on an electric motor that runs at 1700 revolutions per minute is connected by a belt to a four-inch-diameter pulley on a saw arbor. (a) Find the angular speed (in radians per minute) of each pulley. (b) Find the revolutions per minute of the saw.

A sprinkler on a golf green is set to spray water over a distance of 15 meters and to rotate through an angle of \(140^{\circ} .\) Draw a diagram that shows the region that can be irrigated with the sprinkler. Find the area of the region.

The radii of the pedal sprocket, the wheel sprocket, and the wheel of the bicycle in the figure are 4 inches, 2 inches, and 14 inches, respectively. A cyclist is pedaling at a rate of 1 revolution per second. (a) Find the speed of the bicycle in feet per second and miles per hour. (b) Use your result from part (a) to write a function for the distance \(d\) (in miles) a cyclist travels in terms of the number \(n\) of revolutions of the pedal sprocket. (c) Write a function for the distance \(d\) (in miles) a cyclist travels in terms of the time \(t\) (in seconds). Compare this function with the function from part (b). (d) Classify the types of functions you found in parts (b) and (c). Explain your reasoning.