Transition #1 – Before and After

1. Transition #1 – Before and After • “Can a buy a vowel?” game show; small desert offered at many Chinese restaurants. • Actor who starred in Mission Impossible:Ghost Recon; “auto-pilot” for your car. • Cat & Mouse cartoon; “Show me the money!!” movie

2. Unit 2 – Learning Goal 1 The Unit Circle

3. Unit Circle What coordinate do we have here? • Let’s look at the x-y coordinate system: (5, 2) 2 units 5 units

4. Unit Circle • Now let’s zoom in on our graph:

6. 1 We are zoomed in around the origin from (-1, -1) to (1, 1) 1 -1 -1

7. 1 The UNIT CIRCLE is a circle of radius one (1) unit, mapped on the x-y coordinate system. 1 -1 -1

8. 1 (0, 1) What coordinate do we have at this spot? What coordinate do we have at this spot? What coordinate do we have at this spot? We can find the coordinates of certain spots on the circle that are pretty easy to find. What coordinate do we have at this spot? 1 (-1, 0) -1 (1, 0) (0, -1) -1

9. 1 What did we form with our arrows? What coordinate do we have at this spot? How big is the radius of our circle? How big then is our black line? We need to find our x-distance and our y-distance to find the coordinate. What happens if we rotate our point 45° from (1, 0) 1 45° -1 (1, 0) -1

10. 1 Fill in what we know on our triangle. Based off your Partner Investigation, what should x and y equal? _√2_ 2 1 unit y 45° 1 45° x _√2_ 2 -1 So the coordinate that coresponds to a 45° rotation is ( , ) _√2_ 2 _√2_ 2 -1

11. 1 Draw our triangle. Based off your Partner Investigation, what should x and y equal? What coordinate would we have after a 135° rotation?. _√2_ 2 1 unit y 45° 1 Now since we moved left in the x-direction, what sign does our x-coordinate need to have? 45° x _√2_ 2 -1 So the coordinate that coresponds to a 45° rotation is (– , ) _√2_ 2 _√2_ 2 -1

12. 1 (0,1) We can now fill in our “45°” UNIT CIRCLE with angles and the corresponding coordinate. ( ) – √2 , √2 2 2 ( ) √2 , √2 2 2 2 4  2 3 4 1 4 90° 45° 135° 1 8 4 4 4 2 (1,0) (-1,0)  180° 0° 360° -1 315° 225° 7 4 270° 5 4 6 4 3 2 ( ) √2 , – √2 2 2 ( ) – √2 , – √2 2 2 -1 (0,-1)

13. Transition #2 – Guess the Common Phrase • Between a rock and …. • It’s not over until…. • I’m so hungry, I could…. • All that glitters…. • Keep your friends close, and your enemies…

14. 1 We can now do the same thing for our 30° UNIT CIRCLE . _1_ 2 1 unit Based off your Partner Investigation, what should x and y equal? 60° y 1 30° x _√3_ 2 -1 So the coordinate that coresponds to a 30° rotation is ( , ) _√3_ 2 _1_ 2 -1

15. 1 We can now do the same thing for our 60° rotation also. _√3_ 2 1 unit 30° y Based off your Partner Investigation, what should x and y equal? 1 60° x _1_ 2 -1 So the coordinate that coresponds to a 60° rotation is ( , ) _1_ 2 _√3_ 2 -1

16. Based off your Partner Investigation, what should x and y equal? 1 We can now do the same thing for our 150° rotation. 1 unit _1_ 2 60° y 1 30° x _√3_ 2 -1 So the coordinate that coresponds to a 150° rotation is ( , ) –√3_ 2 _1_ 2 -1

17. 1 (0,1) We can now fill in our “30°” UNIT CIRCLE with angles and the corresponding coordinate. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) -1_, -√3 2 2 1_, -√3 2 2 √3, 1_ 2 2 1_, √3 2 2 √3, -1_ 2 2 -√3, 1 2 2 -1_, √3 2 2 -√3, -1_ 2 2 90° 120° 60° 1 150° 30° (1,0) (-1,0) 180° 0° -1 330° 210° 240° 300° 270° -1 (0,-1)

18. PARTNER ACTIVITY #1 • With a partner discuss patterns you see develop on the 45° Circle • Angles in Radian Measure • (x,y) coordinates • Positives/Negatives

19. PARTNER ACTIVITY #2 • With a partner discuss patterns you see develop on the 30° Circle • Angles in Radian Measure • (x,y) coordinates, which goes where • Positives/Negatives