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Animation 104

Animation 104
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2016-08-21 00:23
AngleTrigonometryTransformation
This example demonstrates the change of an angle. Key mathematical concepts include angles, cosine functions, and rotation transformations. Using GeoGebra commands such as Angle, Rotate, and Dilate, the dynamic change of the angle and its relationship with the cosine function are shown. Suitable for high school mathematics education, particularly in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Segment(A, B) → g_1
  2. Line(A, B) → f
  3. Ray(A, B) → g
  4. Point(g_1) → C
  5. OrthogonalLine(C, g) → h
  6. Point(h) → D
  7. Ray(C, D) → i
  8. Point(i) → E
  9. Polygon(A, C, E) → poly1, e, a, c
  10. Segment(A, C) → j
  11. Segment(C, E) → k
  12. Segment(E, A) → l
  13. Min({j, k, l}) → b
  14. Circle(A, (0.2 * b)) → d
  15. Circle(E, (0.2 * b)) → p
  16. Circle(C, (0.2 * b)) → q
  17. Intersect(e, j) → F
  18. Intersect(d, l) → G,
  19. Intersect(d, j) → H,
  20. Intersect(q, j) → I,
  21. Intersect(q, k) → J,
  22. Intersect(p, l) → K,
  23. Intersect(p, k, 1) → L
  24. CircleSector(A, H, G) → r
  25. CircleSector(E, K, L) → s
  26. CircleSector(C, J, I) → t
  27. Ray(C, B) → n
  28. Rotate(t, If[0 < m ≤ 1, ((-m) * π / 2), ((-π)) / 2], C) → t'
  29. Dilate(E, If[1 < m ≤ 2, 2 - m, 0], C) → E'
  30. Vector(E, E') → u
  31. Translate(s, u) → s'
  32. Line(E, n) → f_1
  33. Point(f_1) → M
  34. Angle(M, E, K) → α
  35. Rotate(s', If[2 < m ≤ 3, ((-(m - 2)) * (π / 2 + α)), (-(π / 2 + α))], C) → s''
  36. Midpoint(A, C) → N
  37. Dilate(A, If[3 < m ≤ 4, 4 - m, 0], N) → A'
  38. Vector(A, A') → v
  39. Translate(r, v) → r'_1
  40. Rotate(r'_1, If[4 < m ≤ 5, ((m - 4) * (π - α)), π - α], N) → c_1
  41. Dilate(N, If[5 < m ≤ 6, 6 - m, 0], C) → N'
  42. Vector(N, N') → w
  43. Translate(c_1, w) → d_1