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Unit Circle Trace Demo

Unit Circle Trace Demo
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2019-11-03 03:30
CircleTrigonometryCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the locus of points on a unit circle and its related geometric properties. It involves core mathematical concepts such as the unit circle, trigonometric functions, locus, and analytical geometry. The construction utilizes GeoGebra commands and objects like Mirror, Segment, Circle, Point, OrthogonalLine, Intersect, Angle, CircleArc, Length, Sequence, Translate, Rotate, Line, and If. It is suitable for high school mathematics teaching, helping students understand the relationship between trigonometric functions, geometric shapes, and locus problems.

GeoGebra Commands & Parameters

  1. Mirror(A_0, O) → E_0
  2. Segment(E_0, A_0) → b
  3. Circle(O, A_0) → circ
  4. Point(circ) → A
  5. OrthogonalLine(A, b) → a
  6. Segment(O, A) → hyp
  7. Intersect(a, b) → B
  8. Segment(B, A) → s
  9. Angle(A_0, O, A) → α
  10. Segment(O, B) → c
  11. Segment(C, CS_0) → cc
  12. CircleArc(O, A_0, A) → d
  13. Segment(C_1, C) → dd
  14. Length(d) → lend
  15. Point(d) → D
  16. Segment(S_1, S) → e
  17. Segment(CS_0, S) → f
  18. Angle(O, B, A) → β
  19. Sequence((((i * r) * π / 2), 0), i, 1, 4) → grad1
  20. Segment(B, A) → i
  21. Translate(Segment[O, Rotate[B, (p * π / 2), O]], Vector[(p * Vector[O, CS_0])]) → j
  22. Rotate(A_0, (α * hyp / Distance[A_0, H]), H) → A'
  23. CircleArc(H, A_0, A') → k
  24. Translate(Rotate[k, (p * π / 2), A'], Vector[(p * Vector[A', C_1])]) → q
  25. Translate(B, Vector[(p * Vector[A, S])]) → B'
  26. Translate(A, Vector[(p * Vector[A, S])]) → A'_1
  27. Segment(B', A'_1) → s'
  28. Translate(Rotate[k, (p * π / 2), A'], Vector[(p * Vector[A', S_1])]) → t_1
  29. OrthogonalLine(A_0, b) → l
  30. Line(O, A) → n
  31. Intersect(l, n) → T_1
  32. If(Defined[T_1], A_0, E_0) → E
  33. Segment(T, (x(T), 0)) → tt
  34. Segment(T, (0, y(T))) → a_1
  35. Translate(Rotate[k, (p * π / 2), A'], Vector[(p * Vector[A', (0, y(T))])]) → c_1
  36. Segment(A_0, T_1) → t
  37. Translate(A_0, Vector[(p * Vector[T_1, T])]) → F
  38. Translate(T_1, Vector[(p * Vector[T_1, T])]) → G
  39. Segment(F, G) → t'
  40. Angle(T_1, E, B) → γ
  41. Sequence(Text[" " + (i / 2) + " π r", (((i * r) * π / 2) - 0.2, -0.5)], i, 1, 4) → grad2