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方向角、余弦与比值

方向角、余弦与比值
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2018-02-03 09:45
向量三角函数解析几何
这个范例演示了方向角、余弦和比值的概念。它涉及三角函数和向量的基本知识。通过旋转、交点、向量等命令，用户可以动态地探索三维空间中向量的方向角和余弦值。适合高中数学教学和学习，特别是解析几何和向量课程。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c_1
  3. Intersect(c_1, xAxis, 2) → Q_1
  4. Rotate(Q_1, θ_., O) → Q
  5. Intersect(yAxis, xAxis) → A
  6. Segment(A, P) → f
  7. OrthogonalLine(P, xOyPlane) → g
  8. Intersect(g, xOyPlane) → C
  9. OrthogonalLine(C, xAxis, space) → h
  10. Intersect(h, xAxis) → D
  11. Segment(A, D) → i
  12. Segment(D, C) → j
  13. Vector(A, P) → u
  14. Angle(D, A, P) → α
  15. Point(yAxis) → B
  16. Point(zAxis) → E
  17. Angle(P, A, E) → γ
  18. Angle(P, A, B) → β
  19. Length(i) → x_.
  20. Length(j) → y_.
  21. OrthogonalLine(P, xAxis, space) → l
  22. OrthogonalLine(P, zAxis, space) → m
  23. OrthogonalLine(P, yAxis, space) → n
  24. Intersect(l, xAxis) → F
  25. Intersect(m, zAxis) → G
  26. Intersect(n, yAxis) → H
  27. Segment(F, A) → p
  28. Segment(A, G) → q
  29. Intersect(γ, yAxis, 1) → I
  30. Intersect(yAxis, xAxis) → J
  31. Segment(H, A) → s
  32. Segment(P, F) → t
  33. Segment(G, P) → c
  34. Segment(H, P) → d
  35. Length(p) → a_.
  36. Length(s) → b_.
  37. Length(q) → c_.
  38. Midpoint(A, F) → K
  39. Midpoint(A, H) → L
  40. Midpoint(A, G) → M
  41. Midpoint(f) → N
  42. Angle(Q_1, O, Q) → θ_…
  43. Segment(O, Q) → f_1
  44. OrthogonalLine(Q, xAxis) → g_1
  45. Intersect(g_1, xAxis) → R
  46. Segment(Q, R) → h_1
  47. Segment(R, O) → i_1
  48. Midpoint(i_1) → S
  49. Midpoint(h_1) → T
  50. Vector(R, Q) → w
  51. Vector(O, R) → u_1
  52. Segment(P, C) → j_1
  53. Segment(A, C) → k_1
  54. Angle(A, C, P) → δ
  55. Angle(A, D, C) → ε