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Exploration of Symmetry of Reference Angles

Exploration of Symmetry of Reference Angles
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2018-03-02 12:11
TrigonometryTransformationGeometric Construction
In collections What is a Radian Anyway?
This example demonstrates the symmetry of reference angles. It involves trigonometric functions and geometric transformations. Using GeoGebra commands such as Intersect, Rotate, and Segment, a series of symmetric reference angles can be constructed. Suitable for high school mathematics education, particularly in trigonometry and geometric transformations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Intersect(c, xAxis, 2) → B
  3. Intersect(c, yAxis, 2) → C
  4. Intersect(c, yAxis, 1) → E
  5. Rotate(B, 10°, A) → B'
  6. Rotate(B', 10°, A) → B''
  7. Rotate(B'', 10°, A) → B'''
  8. Rotate(B''', 10°, A) → F
  9. Rotate(F, 10°, A) → F'
  10. Rotate(F', 10°, A) → F''
  11. Rotate(F'', 10°, A) → F'''
  12. Rotate(F''', 10°, A) → G
  13. Rotate(C, 10°, A) → C'
  14. Rotate(C', 10°, A) → C''
  15. Rotate(C'', 10°, A) → C'''
  16. Rotate(C''', 10°, A) → H
  17. Rotate(H, 10°, A) → H'
  18. Rotate(H', 10°, A) → H''
  19. Intersect(c, xAxis, 2) → D
  20. Rotate(D, 10°, A) → D'
  21. Rotate(D', 10°, A) → D''
  22. Rotate(D'', 10°, A) → D'''
  23. Rotate(D''', 10°, A) → J
  24. Rotate(J, 10°, A) → J'
  25. Rotate(J', 10°, A) → J''
  26. Rotate(J'', 10°, A) → J'''
  27. Rotate(J''', 10°, A) → K
  28. Rotate(K, 100°, A) → K'
  29. Rotate(H'', 10°, A) → H'''
  30. Rotate(H''', 10°, A) → I
  31. Rotate(K, 20°, A) → K'_1
  32. Rotate(K'_1, 10°, A) → L
  33. Rotate(L, 10°, A) → L'
  34. Rotate(L', 10°, A) → L''
  35. Rotate(L'', 10°, A) → L'''
  36. Rotate(L''', 10°, A) → M
  37. Rotate(M, 10°, A) → M'
  38. Rotate(M', 10°, A) → M''
  39. Rotate(B, 45°, A) → B'_1
  40. Rotate(C, 45°, A) → C'_1
  41. Rotate(D, 45°, A) → D'_1
  42. Rotate(E, 45°, A) → E'
  43. Segment(B''', D''') → f
  44. Segment(B'_1, D'_1) → g
  45. Segment(F'', J'') → h
  46. Segment(H'', M) → i
  47. Segment(C'_1, E') → j
  48. Segment(C''', L') → k
  49. Line(D, B) → l
  50. Line(C, E) → m