Page 7 - Student Binder for AP Unit 1 Unit Circle_Neat

AP 1.3b Arc Length and Radian Measure
Name _________________________ Date _____ Class __________

Determine each angular displacement in radians. Round to the nearest tenth.
1. 6 revolutions 2. 4.3 revolutions 3. 85 revolutions

Convert from degrees to radians. State in exact terms as well as a decimal
to nearest tenth.
Degree measure Exact radian measure Approximate radian measure

4. 180̊
5. 75̊
6. 45̊
7. 250̊

Convert from radians to degrees. Round to nearest tenth.
Radian Degree measure Radian measure Degree measure
measure

4. π 7. 30π
6 7

5. π 8. 8
3

6. 16π 9. 6.28
3
Complete the chart - use radians mode. Round to nearest hundredth.

Angle Radius Arc Length Angle Radius Arc length
10. 5π 4 13. 82ᵒ 7.3 km
8

11. 6 π cm 14. 14 yd 712 yd
3
12. 11π 2.189 ft 15. 12ᵒ 12 ft
6

13. The position of a point on Earth is often given in terms of latitude and
longitude. Jackson, Mississippi, and St. Louis, Missouri, lie along the same
longitudinal line. The latitude of Jackson is 32ᵒ17’N, and the latitude of St Louis
is 38ᵒ37’N. The radius of Earth is about 4000 miles. About how far apart are the
two cities?
14. (Stretch) Circles A, B, and C each have radius 1. Circles A and B share one
point of tangency. Circle C has a point of tangency with the midpoint of segment
AB. What is the area inside circle C but outside circle A and circle B?