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动画演示三角函数与圆锥

动画演示三角函数与圆锥
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2016-12-01 09:30
函数三角函数立体几何几何作图
①本范例通过动画演示了正弦函数与圆锥的几何关系；②涉及核心数学概念包括三角函数、直角三角形、线性函数、圆锥、正弦值和几何变换；③作图要点运用了CircleArc, Point, Circle, Intersect, Ray, CircleSector, Mirror, Angle, Dilate, Segment, Rotate, Polygon等GeoGebra命令；④适合高中数学教学，用于理解三角函数与立体几何的关联。

GeoGebra 命令及参数

  1. CircleArc(B, A, J) → f_1
  2. CircleArc(B, A, I) → p
  3. Point(p) → C
  4. Circle(B, A) → c
  5. Intersect(f, h) → D
  6. Ray(B, C) → i
  7. CircleArc(B, I, A) → q
  8. CircleArc(B, E, G) → e
  9. Intersect(e, i, 1) → H
  10. CircleSector(B, E, H) → k
  11. Mirror(C, j) → C'
  12. Mirror(H, j) → H'
  13. Angle(E, B, H) → α
  14. Dilate(B, If[0 < b ≤ 1, 1 - b, 0], D) → B'
  15. Segment(B, B') → l
  16. Angle(C, D, B) → β
  17. Mirror(D, j) → D'
  18. Mirror(C, j) → C'_1
  19. Angle(B, D, C') → γ
  20. Rotate(E, If[1 < b ≤ 2, ((b - 1) * α), α], B) → E'
  21. Mirror(E', j) → E''
  22. CircleSector(B, E, E') → r
  23. CircleSector(B, E'', E) → s
  24. Circle(B, 1) → d
  25. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C) → B'_1
  26. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C'_1) → B'_2
  27. CircleArc(B, C', C) → c_1
  28. CircleSector(B, C, C') → d_1
  29. Polygon(B, D, C) → poly1, c_2, b_1, d_2
  30. Polygon(B, C', D) → poly2, d_3, b_2, c'
  31. Circle(B, A) → e_1
  32. Dilate(D, If[1 < b ≤ 2, 2 - b, 0], C) → D'_1
  33. Segment(D, D'_1) → m
  34. Mirror(D'_1, y = 0) → K
  35. Point(m) → L
  36. Rotate(D, If[2 < b ≤ 3, ((-(b - 2)) * π), (-π)], D) → D'_2
  37. Rotate(D'_1, If[2 < b ≤ 3, ((-(b - 2)) * π), (-π)], D) → M
  38. Segment(D'_2, M) → m'
  39. Segment(B, C) → n
  40. Point(n) → N
  41. Segment(N, C'_1) → t