91Ó°ÊÓ

Sketch the graph of the function. (Include two full periods.) $$y=2 \cos x-3$$

Use the graph of the function to determine whether the function is even, odd, or neither. Verify your answer algebraically. $$f(x)=\sec x$$

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).

Describing a Transformation \(g\) is related to a parent function \(f(x)=\sin (x)\) or \(f(x)=\cos (x)\) (a) Describe the sequence of transformations from \(f\) to \(g\). (b) Sketch the graph of \(g .\) (c) Use function notation to write \(g\) in terms of \(f\) $$g(x)=\sin (2 x+\pi)$$

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

You are skiing down a mountain with a vertical height of 1500 feet. The distance from the top of the mountain to the base is 3000 feet. What is the angle of elevation from the base to the top of the mountain?

A car's rear windshield wiper rotates \(125^{\circ} .\) The total length of the wiper mechanism is 25 inches and wipes the windshield over a distance of 14 inches. Find the area covered by the wiper.

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.

A tapered shaft has a diameter of 5 centimeters at the small end and is 15 centimeters long (see figure). The taper is \(3^{\circ} .\) Find the diameter \(d\) of the large end of the shaft.

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.