Download Unit 3 radians and unit circle review

Trigonometry
Radian Measure and the Unit Circle Review
Name
Pd _________
UQ: How are radians and degrees related and what is their relationship to the unit circle?
Covered Concepts:
 What is a radian measure and how do you convert between degrees and radians?
 How are radians used to find arc length and the area of circular sector?
 How are radians used to find linear speed and angular speed?
 How can reference angles be determined?
 How can the unit circle be developed?
 How can the unit circle be used to find the values of trigonometric functions of angles
measured in degrees and radians?
1. Draw a graph which shows a -100o angle sketched in standard position.
2. In which quadrant does the terminal side of a 193o angle lie?
A. First quadrant
B. Second quadrant
C. Third quadrant
D. Fourth quadrant
3. Find the exact value of cos 210o and sin 210o.
4. What is 260o in radians? Express your answer in terms of π.
5. What is the measure of
5
radians equivalent to in degrees?
7
7𝜋
7𝜋
6. Find the exact values of the following: 𝑐𝑜𝑠 ( 4 ) and 𝑠𝑖𝑛 ( 4 )
7. Use the circle below. Find the length s to the nearest tenth. The radius of 2 is in inches.
8. A Ferris wheel has a radius of 75 feet. Two particular cars are located such that the central angle
between them is 155o. To the nearest tenth, what is the length of the intercepted arc between those
two cars on the Ferris Wheel?
For 9 - 11, list the reference angle and state the exact value using the unit circle.
9. sin 300°
10. cos 240°
11. tan 135°
Ref angle ________
_________
________
Quad
________
________
________
Value
_________
_________
________
For #12-16 round your answers to the nearest thousandth and make sure that you include units.
12. What is the degree measure of an angle of 5.72 radians?
13. Find the measure of an angle, in radians, whose intercepted arc is 10 inches in a circle whose radius is 17
inches.
14. A sprinkler has a 22 foot spray and covers an angle of 70o. Draw a diagram that represents this situation
and find the area that the sprinkler waters.
15. A light house in the middle of a channel rotates its light in a circular motion with constant speed. If the
beacon of light completes one rotation every 20 seconds, what is the angular speed of the beacon in radians
per minute?
16. Barbara’s hands go in an 7-inch radius circular pattern as she rows her boat across Echo Lake. If her hands
make a complete rotation every 2.3 seconds, what are the angular speed and linear speed of her hands?
17. The smaller gear in the diagram below has a radius of 2 inches and the larger gear has a radius of 5.7
inches. If the smaller gear rotates 150 degrees, how many degrees has the larger gear rotated?