Name:______
Module 7 Review
1. The measure of an angle is 2.6 radians. If the vertex of the angle is at the center of a circle of radius r, write a formula that defines the relation between r and the arc length s (the arc formed by angle .
2. Suppose that a “flip” is a unit of angle measure where a rotation of 21 flips creates an arc that is a full circle. 3.9 flips is approximately the same angle measure as:
a. How many degrees?
b. How many radians?
3. A spider is clinging to the tip of a fan blade on a wind farm. The fan blade is 35meters long and rotates 4.8 radians counter-clockwise from the 3 o’clock position before coming to a stop. How many meters is the spider above (+) or below (–) the horizontal diameter of the circle traced out by the tip of the blade when it stops?
4. Suppose a skier is circling a track with a 4 km radius as shown below. After leaving the starting point, the skier travels counter-clockwise for 2.7 km. What are the x and y coordinates of the skier’s location on this circle of radius 4 km?
5. Write an equation that could represent the graph to the right.
6. During the Industrial Revolution water wheels provided power to run factories.
a. Given the diagram below, sketch a graph of the height of the bucket above the ground (in feet) as a function of the distance the bucket has traveled in radius lengths. (Label the axes with the quantities being related.)
b. Write a functionf that defines the bucket’s distance to the right of the vertical diameter (in radius lengths) as a function of the angle of rotation of the bucket measured in radians. Define the variables used in your formula.
11. Given
a. What is the input quantity to the tangent function f? (Be specific about the convention used to measure this quantity.)
b. What is the output quantity of the tangent function?
c. What is the range of f?
d. Give an example of a value that is not in the domain of the function , and explain why this is so.
12. The hour hand on a particular clock has a length of 7 inches. What is the change in the vertical distance of the tip of the hour hand (in inches) as the hour hand sweeps from 7 o’clock to 10 o’clock.
13. When an angle measure of 3.2 radians is swept out, the arc length is 12.4 feet. How long is the radius of this circle?
14. Ana is sitting in the bucket of a Ferris wheel. She is exactly 46.7 feet from the center and is at the 3 o’clock position as the Ferris wheel starts turning.
a. If Ana swept out 2.58 radians on a circular arc as the Ferris wheel rotates, how many feet did she travel?
b. Define a function to express the number of feet Ana travels on this Ferris wheel as a function of the number of radians swept out by Ana.
15. a. As varies from to , how does vary?
b. As varies from to , how does vary?
c. As varies from to , how does vary?
16. Suppose Matthew determined that it takes 75 seconds for him to complete one revolution on a Ferris wheel. Determine the speed that Mathew travels when riding the Ferris wheel in radians/second.
17. Determine values of from that make the following statements true.
a.
b.
c.
d.
e.
18. An arctic village maintains a circular cross-country ski trail that has a radius of 2.5 kilometers. A skier started skiing from position , measure in kilometers, and skied counter-clockwise for 3.927 kilometers, where he paused for a brief rest. Determine the ordered pair (in both kilometers and radii) on the coordinate axes that identifies the location where the skier rested.