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THE UNIT CIRCLE

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. From Geometry. if 2s = 1. 2s. 60 o. s. s = ½. 30 o. 90 o.

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THE UNIT CIRCLE

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  18. (0, 1) 900 600 1200 450 1350 1500 300 (-1, 0) (1, 0) 1800 00 , 3600 2100 3300 2250 3150 2400 3000 2700 (0, -1) Jeff Bivin -- LZHS

  19. (0, 1) Walking around by 30o 900 600 1200 1500 300 (-1, 0) (1, 0) 1800 00 , 3600 2100 3300 2400 3000 2700 (0, -1) Jeff Bivin -- LZHS

  20. (0, 1) Walking around by 45o 900 450 1350 (-1, 0) (1, 0) 1800 00 , 3600 2250 3150 2700 (0, -1) Jeff Bivin -- LZHS

  21. Walking around by 60o 600 1200 (-1, 0) (1, 0) 1800 00 , 3600 2400 3000 Jeff Bivin -- LZHS

  22. (0, 1) 900 600 1200 450 1350 1500 300 (-1, 0) (1, 0) 1800 00 , 3600 2100 3300 2250 3150 2400 3000 2700 (0, -1) Jeff Bivin -- LZHS

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

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

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

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

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

  28. (0, 1) Putting it all together! 900 600 1200 450 1350 1500 300 (-1, 0) (1, 0) 1800 00 , 3600 2100 3300 2250 3150 2400 (0, -1) 3000 2700 Jeff Bivin -- LZHS

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