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THE UNIT CIRCLE

This educational resource, developed by the LZHS Advanced Math Team and edited by Jeff Bivin, provides an in-depth exploration of the Unit Circle. It covers essential concepts including angles, radians, and coordinates associated with key angles like 30°, 45°, and 60°. The document also explains how to calculate sine and cosine values for various angles and discusses their geometric interpretations. Ideal for high school students, this guide enhances comprehension of circular functions and lays a strong foundation for further studies in trigonometry.

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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 2s 60o s 30o 90o if 2s = 1 60o s = ½ 90o 30o 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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