91Ó°ÊÓ

Find the radian measure of the central angle of a circle of radius \(r\) that intercepts an arc of length \(s\). Arc Length s 6 inches 8 feet 25 centimeters 160 kilometers 14 feet

Explain how reference angles are used to find the trigonometric functions of obtuse angles.

Sound Waves Sound waves can be modeled by sine functions of the form \(y=a \sin b x\), where \(x\) is measured in seconds. (a) Write an equation of a sound wave whose amplitude is 2 and whose period is \(\frac{1}{264}\) second. (b) What is the frequency of the sound wave described in part (a)?

Define the inverse cotangent function by restricting the domain of the cotangent function to the interval \((0, \pi)\), and sketch its graph.

Define the inverse secant function by restricting the domain of the secant function to the intervals \([0, \pi / 2)\) and \((\pi / 2, \pi]\), and sketch its graph.

Linear and Angular Speeds A \(7 \frac{1}{4}\)-inch circular power saw rotates at 5200 revolutions per minute. (a) Find the angular speed of the saw blade in radians per minute. (b) Find the linear speed (in feet per minute) of one of the 24 cutting teeth as they contact the wood being cut.

Linear and Angular Speeds A carousel with a 50-foot diameter makes 4 revolutions per minute. (a) Find the angular speed of the carousel in radians per minute. (b) Find the linear speed of the platform rim of the carousel.

Speed of a Bicycle 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 part (b). (d) Classify the types of functions you found in parts (b) and (c). Explain your reasoning.

A group of people agree to share equally in the cost of a \(\$ 250,000\) endowment to a college. If they could find two more people to join the group, each person's share of the cost would decrease by \(\$ 6250\). How many people are presently in the group?

Your football has landed at the edge of the roof of your school building. When you are 25 feet from the base of the building, the angle of elevation to your football is \(21^{\circ}\). How high off the ground is your football?