Advanced Math/Trigonometry Review 3.1 – 3.3
PA Standards: 2.3
Anchors: A2; B1
7
1. Find the degree measure for a 5 rotation counterclockwise and sketch the angle in standard
position.
y
x
2. Find the degree measure for a
position.
11
5
rotation clockwise and sketch the angle in standard
y
x
3. Express 32.27 in degrees-minutes-seconds.
4. Express -28.45 in degrees-minutes-seconds.
5. Identify (a) all angles coterminal with an angle of -225 and (b) the coterminal angle whose
measure is between 0 and 360.
6. Identify (a) all angles coterminal with an angle of 758 and (b) the coterminal angle whose
measure is between 0 and 360.
7. A gear rotates at a rate of 675 rotations per minute. Through how Many degrees does it rotate in 1
second?
8. A gear rotates at a rate of 438 rotations per minute. Through how Many degrees does it rotate in 1
second?
9. Express 260 in radians. Give the answer in terms of .
10. Express -190 in radians. Give the answer in terms of .
11. Express 5.4 in degrees.
12. Express -7.8 in degrees.
13. Express 4.2 in degrees. Round the answer to the nearest tenth of a degree.
14. Express -5.3 in degrees. Round the answer to the nearest tenth of a degree.
15. Determine the arc length to the nearest tenth of a meter of a circle of radius 0.7 m that is
intercepted by a central angle of 210.
16. Determine the arc length to the nearest tenth of a meter of a circle of radius 1.3 m that is
intercepted by a central angle of 150.
17. A pendulum swings through an angle of 50, describing an arc 0.45 m long. Determine the
length of the pendulum to the nearest hundredth of a meter.
18. A pendulum swings through an angle of 130, describing an arc 1.3 m long. Determine the
length of the pendulum to the nearest hundredth of a meter.
19. Determine the area of a sector of a circle of radius 2.1 m intercepted by a central angle of 95.
20. Determine the area of a sector of a circle of radius 3.5 cm intercepted by a central angle of 55.
21. A gear makes 7.8 rotations about its axis. What is the angular displacement in radians of a point
on the gear?
22. A gear makes 4.2 rotations about its axis. What is the angular displacement in radians of a point
on the gear?
23. What is the angular velocity in radians per minute of a notch on a wheel that makes 27 rotations
per second about its axis?
24. What is the angular velocity in radians per minute of a notch on a wheel that makes 68 rotations
per second about its axis?
25. Find the angular velocity in radians per second of a wheel turning at 275 rpm.
26. Find the angular velocity in radians per second of a wheel turning at 435 rpm.
27. Determine the linear velocity of a point located 5 cm from the center of a wheel rotating at
18 rad/sec.
28. Determine the linear velocity of a point located 9 cm from the center of a wheel rotating at
27 rad/sec.
29. The minute hand of a watch is 1.8 cm long. What is the linear velocity of the tip of this hand?
30. The minute hand of a watch is 0.6 cm long. What is the linear velocity of the tip of this hand?
31. A gear rotates at 27 rps. Find the linear velocities of the points (a) 2.5 cm and (b) 7.9 cm from the
center of the gear.
32. A gear rotates at 32 rps. Find the linear velocities of the points (a) 1.7 cm and (b) 5.6 cm from the
center of the gear.