1. Definition y
Radian: The length of the arc above the angle divided by the radius of the circle. x
in radians ,

2. Definition y x Unit Circle: the circle with radius of 1 unit 1
If r=1, =s
in radians ,

3. Definition
The radian measure of an angle is the distance traveled around the unit circle. Since circumference of a circle is r and r=1, the distance around the unit circle is 2

4. Important Idea
If a circle contains 360° or 2 radians, how many radians are in 180°
Use to change rads to degrees
180°
rads
Use to change degrees to rads
rads
180°

5. Try This
Change 240° to radian measure in terms of .

6. Try This
Change radians to degree measure.
157.5°

7. Try This
Change radians to degree measure.
171.89°

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

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

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

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

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

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

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

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

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

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

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

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

20. Definition
The quadrantal angles in radians

21. Definition
The quadrantal angles in radians

22. Definition
The quadrantal angles in radians

23. Definition The quadrantal angles in radians
The terminal side is on an axis.

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

25. Important Idea
To find coterminal angles, simply add or subtract either 360° or radians to the given angle or any angle that is already coterminal to the given 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. Try This
Find 3 angles coterminal with 60°
420°,780° and -300°

31. Try This
Find two positive angle and one negative angle coterminal with radians.
and ,