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Place a Radian Angle on the Unit Circle

Place a Radian Angle on the Unit Circle
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2020-03-03 00:50
CircleAngleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to place and visualize a radian angle on the unit circle. It involves core math concepts like angles, the unit circle, trigonometry, and coordinate geometry. Construction highlights include commands like Random, Corner, Element, If, Circle, Intersect, Sequence, CircleArc, Point, Vector, Polygon, Take, Segment from GeoGebra. Suitable for high school students learning about trigonometric functions and the unit circle, ideal for classroom instruction or self-study.

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, "", If[Num ≟ -1, "", Num + ""]]) → Textnum
  7. If(ChoixDen ≟ 1, Textnum, Textnum + "π/" + 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. Take(liste1, 1, 6) → liste5
  20. Sequence(Text["" + " π / " + (12 - k), Element[liste5, k] + (0.2, 0.1)], k, 1, 6) → liste6
  21. If(ChoixDen ≟ 1, Textnum, Textnum + "π") → texte11
  22. If(ChoixDen ≟ 1, Textnum, ChoixDen + " ") → texte12
  23. Segment(L, M) → e