1. October 13, 2011 At the end of today, you will be able to: Describe angles and use radian and degree measures. Warm-up: With a partner brainstorm what you remember about the following: 1.Sketch a positive and a negative angle on two separate graphs. 2.What are complementary and supplementary angles? Give some examples. 3.In which quadrant is the terminal side of a 225° angle? 4.What is 1 radian? Be prepared to teach the class what you remember!

2. Angles in the coordinate plane Most of our angles will be in “standard position” – starting on the positive x-axis. The initial side of the angle The terminal side of the angle The angle measure

3. Common Angles 90° 180° 270° 360°

4. Positive angles (counterclockwise) Negative angles (clockwise) The initial side always stays on the x-axis.

5. Negative Angles -90° -180° -270° -360°

6. Make a sketch of the following angles: 1. 30° 2. 120° 3. 325° 4. -45° 5. -225° 6. -135°

7. Coterminal Angles: α + 360k Angles that have the same initial and terminal sides, but not the same angles. Example 1: Coterminal angles for 210° α + 360k, k is the number of rotations When α = 210, 210 + 360(1) = 210 + 360(-1) = Name 2 coterminal angles for 0°. You try: Determine two coterminal angles (one positive and one negative) for 45° and -36°. 570° -150°

8. So long, Degrees! Hello, Radians! What is a Radian? r = the radius of the circle r r s = r θ One radian is the measure of the angle, θ, when the radius, r, is equal to the length of the arc, s.

9. Understanding Radians The unit circle is a circle with a radius of 1. Two things to recall: It is 360° to go around the entire circle. Circumference = 2πr So… 360° = 2π(1) 360° = 2π radians r = 1 360° = 2π 90° = 180° = π 270° =

10. Common Angles 90°= 180° = π 270° = 360° = 2π

12. Degrees to Radians When converting from degrees to radians, multiply Example: Convert 125° to radians. 125 Reduce and leave as a fraction.

13. Go back to this slide, and rewrite the angles in radians. 1. 30° 2. 120° 3. 325° 4. -45° 5. -225° 6. -135°

14. Now let’s go the other way around… Radians to Degrees Example: Convert to degrees. Multiply 36 = 144° Your Turn!!! Convert There’s a shorter way! Ask me.

15. Classwork Pg. 290 #4, 13, 17, 31, 47, 52

16. Common Angles in Radians