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Circular Motion and Piecewise Functions - Advanced Trigonometry

Circular Motion and Piecewise Functions - Advanced Trigonometry
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2019-12-24 04:55
CircleFunctionTrigonometryCoordinate Geometry
This example demonstrates the relationship between a point moving along a circular path and the graph of a piecewise function. It involves core mathematical concepts such as circles, coordinate geometry, trigonometric functions, piecewise functions, rotation, and reflection. The construction uses GeoGebra commands/objects like Segment, Circle, Vector, Translate, Mirror, and Dilate. Suitable for high school and advanced learners to understand the connection between complex function graphs and geometric transformations.

GeoGebra Commands & Parameters

  1. Segment(J, K) → f
  2. Segment(L, M) → g
  3. Circle(A, R) → c
  4. Vector((0, 0), (U1, U2)) → u
  5. Translate(c, u) → c'
  6. Translate(L, u) → L'
  7. Translate(M, u) → M'
  8. Segment(L', M') → g'
  9. Translate(J, u) → J'
  10. Translate(K, u) → K'
  11. Segment(J', K') → f'
  12. Translate(N, u) → N'
  13. Translate(O, u) → O'
  14. Translate(P, u) → P'
  15. Translate(Q, u) → Q'
  16. Translate(S, u) → S'
  17. Translate(T, u) → T'
  18. Translate(U, u) → U'
  19. Translate(A, u) → A'
  20. Mirror(N', ligning1) → N''
  21. Mirror(P', ligning1) → P''
  22. Mirror(Q', ligning1) → Q''
  23. Mirror(T', ligning1) → T''
  24. Mirror(U', ligning1) → U''
  25. Dilate(c', T3, A') → c''
  26. Dilate(L', T3, A') → L''
  27. Dilate(M', T3, A') → M''
  28. Segment(L'', M'') → g''
  29. Dilate(J', T3, A') → J''
  30. Dilate(K', T3, A') → K''
  31. Segment(J'', K'') → f''
  32. Dilate(N', T3, A') → N''_1
  33. Dilate(N'', T3, A') → N'''
  34. Dilate(O', T3, A') → O''
  35. Dilate(P', T3, A') → P''_1
  36. Dilate(P'', T3, A') → P'''
  37. Dilate(Q', T3, A') → Q''_1
  38. Dilate(Q'', T3, A') → Q'''
  39. Dilate(S', T3, A') → S''
  40. Dilate(T', T3, A') → T''_1
  41. Dilate(T'', T3, A') → T'''
  42. Dilate(U', T3, A') → U''_1
  43. Dilate(U'', T3, A') → U'''
  44. Mirror(N', h) → N''_2
  45. Mirror(N'', h) → N'''_1
  46. Mirror(N''_1, h) → V
  47. Mirror(N''', h) → W
  48. Mirror(O'', h) → O'''
  49. Mirror(O', h) → O''_1
  50. Mirror(Q'', h) → Q'''_1
  51. Mirror(Q', f'') → Q''_2
  52. Mirror(Q''_1, h) → Z
  53. Mirror(Q''', h) → A_1
  54. Mirror(S', h) → S''_1
  55. Mirror(S'', h) → S'''