2. Angles and Their Measure Section 4.1

3. Objectives I can label the unit circle for radian angles I can determine what quadrant an angle is in I can draw and angle showing correct rotation in Standard Format I can calculate Reference Angles

4. Definition of a Radian One radian is the measure of the central angle of a circle that intercepts an arc equal in length to the radius of the circle.

5. Radian Measure Consider an arc of length s on a circle or radius r. The measure of the central angle that intercepts the arc is  = s/r radians.  O r s r

6. Section 4.1: Figure 4.6, Illustration of Six Radian Lengths

7. Section 4.1: Figure 4.7, Common Radian Angles

9. Section 4.1: Figure 4.2, Angle in Standard Position

10. Section 4.1: Figure 4.3, Positive and Negative Angles

11. Angles of the Rectangular Coordinate System An angle is in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side lies along the positive x-axis. x y Terminal Side Initial Side Vertex   is positive Positive angles rotate counterclockwise. x y Terminal Side Initial Side Vertex   is negative Negative angles rotate clockwise.

12. Practice Drawing and Labeling White Board

13. Definition of a Reference Angle A reference angle is the positive acute angle formed by the terminal side of  and the x-axis. ALWAYS Positive ALWAYS less than 90 degrees or π/2 radians

14. Example a b   a b P(a,b) Find the reference angle , for the following angle:  =315º Solution:  =360 º - 315 º = 45 º

15. Example Find the reference angles for:

16. Quadrants What quadrants are the following angles?

17. Homework WS 8-2 Start learning Unit circle radians and degrees