1. Introduction to Trigonometry Angles and Radians (MA3A2): Define an understand angles measured in degrees and radians.

2. the rotating ray and the positive half of the x-axis angle

3. a positive angle whose vertex is at the center of a circle central angle

4. 2 angles with a sum of 90 degrees complementary angles

5. 2 angles in standard position that have the same terminal side coterminal angles

6. The beginning ray of an angular rotation; the positive half of the x- axis for an angle in standard position initial side

7. a clockwise measurement of an angle negative degree measure

8. Moving around a circle toward the right; a negative rotation Clockwise

9. a counterclockwise measurement of an angle positive degree measure

10. Opposite to clockwise; moving around the circle toward the left; a positive rotation counterclockwise

11. An angle in standard position with a terminal side that coincides with one of the four axes quadrantal angle

12. One of the 4 regions into which the x- and y-axes divide the coordinate plane quadrant

13. A unit of angle measure radian

14. The position of an angle with vertex at the origin, initial side on the positive x-axis, and terminal side in the plane standard position

15. 2 angles with a sum of 180 degrees supplementary angles

16. The ending ray of an angular rotation; rotating ray terminal side

17. 1 full revolution Obj: Find the quadrant in which the terminal side of an angle lies. half a revolution

18. ¼ of a revolution Obj: Find the quadrant in which the terminal side of an angle lies. triple revolution

19. Quad. IQuad. II Quad. III Quad. IV 0 ◦ /360° 90 ◦ 180 ◦ 270 ◦

20. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ In which quadrant does the terminal side of the angle lie? EX: 53°

21. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ In which quadrant does the terminal side of each angle lie? EX: 253°

22. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ EX: In which quadrant does the terminal side of each angle lie? EX: -126°

23. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ EX: In which quadrant does the terminal side of each angle lie? EX: -373°

24. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ EX: In which quadrant does the terminal side of each angle lie? EX: 460°

25. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ ON YOUR OWN: In which quadrant does the terminal side of each angle lie? 1. 47° 2. 212° 3. -43° 4. -135° 5. 365°

26. I II III IV 0 ◦/ 360 ◦ 90 ◦ 180 ◦ 270 ◦ ON YOUR OWN: In which quadrant does the terminal side of each angle lie? 1. 47° 2. 212° 3. -43° 4. -135° 5. 365° I III IV IIII

27. ON YOUR OWN: Draw each angle. 7. -90° 6. 45° 8. 225°9. 405°

28. ON YOUR OWN: Draw each angle. 7. -90° 6. 45° 8. 225°9. 405°

29. Θ (theta) Lowercase Greek letters are used to denote angles α (alpha) β (beta) γ (gamma)

30. EX: Θ = 60°. Finding Coterminal Angles (angles that have the same terminal side):

31. EX: Θ = 790°. Finding Coterminal Angles (angles that have the same terminal side): 1)Add and subtract from 360°, OR 2)Add and subtract from 2∏. EX: Θ = 440°. EX: Θ = -855°.

32. 1. Θ = 790°. ON YOUR OWN: Find one positive and one negative coterminal angle.

33. Reference Angle: the acute angle formed by the terminal side and the closest x-axis. EX: Find the reference angle for each angle. Θ = 115°. **Reference angles are ALWAYS positive!! **Subtract from 180° or 360°.

34. Reference Angle: the acute angle formed by the terminal side and the closest x-axis. EX: Θ = 225°. **Reference angles are ALWAYS positive!! **Subtract from 180° or 360°.

35. Reference Angle: the acute angle formed by the terminal side and the closest x-axis. EX: Θ = 330° **Reference angles are ALWAYS positive!! **Subtract from 180° or 360°.

36. EX: Θ = -150°. Finding Reference Angles fpr Negative Angles: 1)Add 360° to find the coterminal angle. 2)Subtract from closest x-axis (180° or 360°).

37. EX: Θ = 60°. **If Θ lies in the first quadrant, then the angle is it’s own reference angle.

38. 11. Θ = 210 ° 10. Θ = 405° 12. Θ = -300 °13. Θ = -225 ° ON YOUR OWN: Find the reference angle for the following angles of rotation.

39. 11. Θ = 210 ° 10. Θ = 405° 12. Θ = -300 °13. Θ = -225 ° ON YOUR OWN: Find the reference angle for the following angles of rotation.

40. Converting Degrees to Radians *Multiply by ∏ radians 180 degrees EX: 60° EX: 225° EX: 300° EX: -315°

41. ON YOUR OWN: Convert to radian measure. Give answer in terms of ∏. 14. 15° 15. 30° 16. 100° 17. -220° 18. -85°

42. ON YOUR OWN: Convert to radian measure. Give answer in terms of ∏. 14. 15° 15. 30° 16. 100° 17. -220° 18. -85°

43. Converting Radians to Degrees *Multiply by 180 degrees ∏ radians EX:

44. ON YOUR OWN: Convert to Degrees 19. 20. 21. 22. 23. -210° -2160° 135° 225° 270°

45. ON YOUR OWN: Convert to Degrees 19. 20. 21. 22. 23.

46. Finding Coterminal Angles *add or subtract from 360° *_____degrees ± 360 EX: 390° EX: 140° EX: -100°

47. Finding Complements and Supplements *To find the complement: subtract from 90° *To find the supplement: subtract from 180° EX: 35°EX: 120°