1. In The Coordinate Plane
ANGLES
In The Coordinate Plane

2. Endpoint
Ray

3. Endpoint
Ray

4. Terminal Side
ANGLE
Endpoint
Initial Side

5. Terminal Side
ANGLE
Vertex
Initial Side

6. An Angle In Standard Position
Initial Side
Vertex

7. The Measure of an Angle
Describes the amount and direction of rotation required to get from the initial side to the terminal side.

8. Counterclockwise has a positive direction

9. Clockwise has a negative direction

10. An Angle in Standard Position
Is said to lie in the quadrant in which its terminal side falls.

11. II I
III IV

12. II I
A Positive Angle
In Quadrant I
III IV

13. II I
III IV

14. II I
A Negative Angle
In Quadrant I
III IV

15. II I
III IV

16. II I
A Positive Angle
In Quadrant II
III IV

17. II I
III IV

18. II I
A Negative Angle
In Quadrant III
III IV

19. II I
III IV

20. II I
A Positive Angle
In Quadrant IV
III IV

21. How Do We
Usually Measure
Angles?
Degrees

23. What Quadrant does this angle in?
It’s Terminal side lies on the positive y-axis
What Quadrant does this angle in?
NO Quadrant

26. What Quadrant does this angle in?
It’s Terminal side lies on the negative x-axis
What Quadrant does this angle in?
NO Quadrant

31. One rotation counterclockwise
Known Fact
One rotation counterclockwise or
1 rot counterclockwise = 360º

32. Example

33. 1 rot counterclockwise = 360º
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Known Fact
1 rot counterclockwise = 360º

34. Positive 270° tells us counterclockwise rotation
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Positive 270° tells us counterclockwise rotation

36. Next
Example

37. Find the degree measure of the angle and draw the angle in standard position.

38. Known Fact
One rotation clockwise

39. Next
Example

40. rot degrees 1 1 rot Known Fact 1 rot clockwise = –360º
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Known Fact
1 rot clockwise = –360º

41. Negative 180° indicates a clockwise rotation
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Negative 180° indicates a clockwise rotation

43. Next
Example

44. 1 rot counterclockwise = 360º
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Known Fact
1 rot counterclockwise = 360º

45. Positive 840° tells us counterclockwise rotation
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Positive 840° tells us counterclockwise rotation

46. Protractor

47. Next
Example

48. rot degrees 1 1 rot Known Fact 1 rot clockwise = – 360º
Find the degree measure of the angle and draw the angle in standard position.
rot
degrees 1 1
rot
Known Fact
1 rot clockwise = – 360º

49. How Do You Know What Quadrant?

50. How Do You Know What Quadrant?

51. How Do You Know What Quadrant?
Protractor
How Do You Know What Quadrant?

52. You
Try

53. Find the degree measure of the angle for each rotation.
Draw the angle in standard position.
State which quadrant or axis on which the terminal side of each angle lies

54. Terminal side lies in the 2nd Quadrant
– 2250
Terminal side lies in the 2nd Quadrant

55. Terminal side lies in the 3rd Quadrant
2160
Terminal side lies in the 3rd Quadrant

56. Terminal side lies in the 4th Quadrant
2800
Terminal side lies in the 4th Quadrant

57. Terminal side lies on the negative y-axis
– 15300
Terminal side lies on the negative y-axis

58. Go The Other Way

59. 1 rot counterclockwise = 360º
450° is how many rotations in which direction?
Positive
rotations 1
Known Fact
1 rot counterclockwise = 360º

60. 1 rot counterclockwise = 360º
450° is how many rotations in which direction? ?
rotations 1
Known Fact
1 rot counterclockwise = 360º

61. 1 rot counterclockwise = 360º
450° is how many rotations in which direction? 1
rot
rotations 1
Known Fact
1 rot counterclockwise = 360º

62. 1 rot counterclockwise = 360º
450° is how many rotations in which direction? 1
rot
rotations 1
Known Fact
1 rot counterclockwise = 360º

63. 450° is how many rotations in which direction?1
rot
rotations 1
Counterclockwise

64. – 1530° is how many rotations in which direction?
You Try

65. – 1530° is how many rotations in which direction?
Clockwise