1. THE UNIT CIRCLE Initially Developed by LZHS Advanced Math Team (Keith Bullion, Katie Nerroth, Bryan Stortz) Edited and Modified by Jeff Bivin Lake Zurich High School jeff.bivin@lz95.org Jeff Bivin -- LZHS

2. 2s s 30 o 90 o 60 o if 2s = 1 s = ½ Jeff Bivin -- LZHS

3. 30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

4. 30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) 150 o Jeff Bivin -- LZHS

5. 30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) 210 o Jeff Bivin -- LZHS

6. 30 o 90 o 60 o (1, 0) (-1, 0) (0, 1) (0, -1) 330 o Jeff Bivin -- LZHS

7. 60 o 90 o 30 o s 2s if 2s = 1 s = ½ Jeff Bivin -- LZHS

8. 60 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o Jeff Bivin -- LZHS

9. 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o 60 o 120 o Jeff Bivin -- LZHS

10. 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o 240 o 60 o Jeff Bivin -- LZHS

11. 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 30 o 300 o 60 o Jeff Bivin -- LZHS

12. 45 o 90 o s s if Jeff Bivin -- LZHS

13. 45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

14. 45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 135 o Jeff Bivin -- LZHS

15. 45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 225 o Jeff Bivin -- LZHS

16. 45 o 90 o (1, 0) (-1, 0) (0, 1) (0, -1) 315 o Jeff Bivin -- LZHS

17. 2x x 30 o 90 o 60 o 90 o 30 o x 2x 45 o 90 o x x (1, 0) (-1, 0) (0, 1) (0, -1) Putting it Together Jeff Bivin -- LZHS

18. 30 0 45 0 60 0 90 0 120 0 135 0 150 0 180 0 210 0 225 0 240 0 270 0 300 0 315 0 330 0 0, 360 0 (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

19. 30 0 60 0 90 0 120 0 150 0 180 0 210 0 240 0 270 0 300 0 330 0 0, 360 0 (1, 0) (-1, 0) (0, 1) (0, -1) Walking around by 30 o Jeff Bivin -- LZHS

20. 45 0 90 0 135 0 180 0 225 0 270 0 315 0 0, 360 0 (1, 0) (-1, 0) (0, 1) (0, -1) Walking around by 45 o Jeff Bivin -- LZHS

21. 60 0 120 0 180 0 240 0 300 0 0, 360 0 (1, 0) (-1, 0) Walking around by 60 o Jeff Bivin -- LZHS

22. 30 0 45 0 60 0 90 0 120 0 135 0 150 0 180 0 210 0 225 0 240 0 270 0 300 0 315 0 330 0 0, 360 0 (1, 0) (-1, 0) (0, 1) (0, -1) Jeff Bivin -- LZHS

23. 0 Divide each semi-circle into 4 parts. Jeff Bivin -- LZHS

24. 0 Can we reduce any of those fractions? Divide each semi-circle into 6 parts. Jeff Bivin -- LZHS

25. 0 Putting the radian measures together! Jeff Bivin -- LZHS

26. 0 Compare to the degree measure  π = 180 o Jeff Bivin -- LZHS

27. 0 (1, 0) (-1, 0) (0, 1) (0, -1) Look at the points! Jeff Bivin -- LZHS

28. 30 0 45 0 60 0 90 0 120 0 135 0 150 0 180 0 210 0 225 0 240 0 270 0 300 0 315 0 330 0 0, 360 0 (1, 0) (0, 1) (-1, 0) (0, -1) Putting it all together! Jeff Bivin -- LZHS