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Unit Circle Beyond 2Pi (Harder)

Unit Circle Beyond 2Pi (Harder)
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2015-10-01 20:21
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the extension and reflection of the unit circle beyond 2π, involving core concepts like the unit circle, reflection, equations, orthocenter, and differential equations. It utilizes GeoGebra commands such as Random, Corner, Element, If, Circle, Intersect, Sequence, CircleArc, Point, Vector, Polygon, and Length. Suitable for high school and advanced learners to explore periodicity and symmetry in trigonometric functions.

GeoGebra Commands & Parameters

  1. Random(1, voirindexMax) → choix
  2. Random(1, IndexMax) → choixindex
  3. Corner(4) → C4
  4. Element(Denominateur, choix) → ChoixDen
  5. Element(Numerateur, choix) → Num
  6. If(Num ≟ 0, "0", If[Num ≟ 1, "\pi", If[Num ≟ -1, "-\pi", Num + "\pi"]]) → Textnum
  7. If(ChoixDen ≟ 1, Textnum, "\frac{" + Textnum + "}{" + ChoixDen + " }") → Anglepi
  8. Element(Rayon, choixindex) → r
  9. Circle((0, 0), 5) → c
  10. Intersect(c, xAxis) → A, B
  11. Sequence(Rotate[B, d°, (0, 0)], d, 15, 360, 15) → liste1
  12. Sequence(Segment[(0, 0), Element[liste1, i]], i, 0, Length[liste1]) → liste2
  13. Sequence(Rotate[B, d°, (0, 0)], d, 45, 360, 45) → liste3
  14. Sequence(Segment[(0, 0), Element[liste3, i]], i, 0, Length[liste3]) → liste4
  15. CircleArc(C, D, E) → d
  16. Point(d) → F
  17. Vector(F, E) → u
  18. Polygon(H, I, J, K) → poly1, h, i, j, k
  19. Length(Denominateur) → b
  20. Length(Numerateur) → e