1. Will Teach you all of you angels how to Angle properly!
Angle Measurement
Mr. Peter Richard
Will Teach you all of you angels how to Angle properly!
Learning Goals:
Extend the definition of an angle to include negative angles and angles greater than 180°

2. Definition y x Terminal Side Vertex A Angle A is in standard position
Initial Side

3. Definition
If the terminal side moves counter-clockwise, angle A is positive y A x

4. Definition
If the terminal side moves counter-clockwise, angle A is positive y A x

5. Definition
If the terminal side moves counter-clockwise, angle A is positive y x A

6. Definition
If the terminal side moves clockwise, angle A is negative y x A

7. Definition
If the terminal side moves clockwise, angle A is negative y x A

8. Definition
If the terminal side moves clockwise, angle A is negative y x A

9. Definition
If the terminal side moves clockwise, angle A is negative x y A

10. Definition y
If the terminal side is on an axis, angle A is a quadrantel angle A x

11. Definition y
If the terminal side is on an axis, angle A is a quadrantel angle A x

12. Definition y
If the terminal side is on an axis, angle A is a quadrantel angle A x

13. Try This
What kind of angle is this? (hint: where is the terminal side?)
quadrantal angle

14. Try This
What is the measure of this angle?
-90°
-45°
-270°
-360°

15. Try This
What is the measure of this angle?
-90°
-45°
-270°
-360°

16. Try This
What is the measure of this angle? 0°
45°
90°
120°
180°

17. Try This
What is the measure of this angle? 0°
45°
90°
120°
180°

18. Try This
What is the measure of this angle?
-90°
-45°
-270°
-360°

19. Try This
What is the measure of this angle?
-90°
-45°
-270°
-360°

20. Try This
What is the measure of this quadrantal angle? x y 0°

21. Try This
If a 143° angle is in standard position, determine the quadrant in which the terminal side lies. x y 2

22. Try This
If a 280° angle is in standard position, determine the quadrant in which the terminal side lies. x y 4

23. Definition
Coterminal Angles: Angles that have the same terminal side.

24. Example
Find positive angles and negative angles that are coterminal with 30°.

25. Important Idea
To find coterminal angles, simply add or subtract 360° to the given angle or any coterminal angle.

26. 30° x y
Analysis
30° and 390° have the same terminal side, therefore, the angles are coterminal y
390° x

27. 30° x y
Analysis
30° and 750° have the same terminal side, therefore, the angles are coterminal x y
750°

28. 30° x y
Analysis
30° and 1110° have the same terminal side, therefore, the angles are coterminal x y
1110°

29. 30° x y
Analysis
30° and ° have the same terminal side, therefore, the angles are coterminal x y
-330°

30. With Mr. Peter Richard
How many angles can you find that are coterminal with a 30° angle and how do you find them?

31. Try This
Find 3 angles coterminal with 60°
420°,780° and -300°

32. Practice
Quiz: Page 722: # 2, 4, 6, 8, 12
Homework: # 1, 3, 5, 11, 15