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单位圆（象限恒等式）

单位圆（象限恒等式）
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2017-05-22 17:59
圆三角函数几何作图
该范例演示单位圆上的象限恒等式。涉及的核心数学概念包括三角函数和单位圆。通过使用GeoGebra命令如Intersect、Circle、Point等，可以构造出单位圆上的点和相关象限角。适合高中数学教学和学习三角函数。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Point(c) → C
  4. Point(Circle[A, 1]) → D
  5. Segment(A, C) → f
  6. OrthogonalLine(C, f) → g
  7. Intersect(g, xAxis) → E
  8. Intersect(g, yAxis) → F
  9. OrthogonalLine(C, xAxis) → j
  10. Intersect(j, xAxis) → G
  11. OrthogonalLine(C, yAxis) → k
  12. Intersect(k, yAxis) → H
  13. Segment(A, H) → l
  14. Segment(A, G) → m
  15. Segment(C, G) → q
  16. Segment(C, H) → r
  17. Angle(C, G, A) → β
  18. Angle(B, A, C) → Θ
  19. Intersect(m, q) → J
  20. Polygon(C, J, A) → poly1, a, c_1, j_1
  21. Ray(A, C) → i
  22. Point(yAxis) → I
  23. Point(xAxis) → K
  24. Segment(I, K) → h
  25. OrthogonalLine(K, h) → n
  26. OrthogonalLine(I, h) → p
  27. Intersect(p, xAxis) → L
  28. OrthogonalLine(L, p) → s
  29. Intersect(n, s) → M
  30. Segment(I, L) → t
  31. Segment(L, M) → b
  32. Segment(M, K) → d
  33. Intersect(i, t) → N
  34. Intersect(i, b) → O
  35. Intersect(i, d) → P
  36. Angle(N, A, L) → α
  37. Angle(L, A, O) → γ
  38. OrthogonalLine(N, yAxis) → e
  39. Intersect(e, h) → Q
  40. Segment(A, Q) → f_1
  41. Intersect(c, f_1, 1) → R
  42. Angle(K, A, R) → δ
  43. OrthogonalLine(R, xAxis) → g_1
  44. Intersect(g_1, xAxis) → S
  45. Segment(A, R) → h_1
  46. Segment(R, S) → i_1
  47. Segment(S, A) → k_1
  48. Ray(O, A) → l_1
  49. Intersect(c, l_1, 2) → T
  50. OrthogonalLine(T, xAxis) → m_1
  51. Intersect(m_1, xAxis) → U
  52. Segment(A, T) → n_1
  53. Segment(T, U) → p_1
  54. Segment(U, A) → q_1
  55. Angle(U, A, T) → ε
  56. OrthogonalLine(P, xAxis) → r_1
  57. Intersect(r_1, h) → V
  58. Segment(A, V) → s_1
  59. Intersect(c, s_1, 1) → W
  60. Segment(A, W) → t_1
  61. Segment(W, J) → a_1
  62. Angle(K, A, W) → ζ
  63. Angle(P, A, K) → η
  64. Intersect(i, b) → H_1
  65. Intersect(i, t) → I_1
  66. Intersect(i, h) → J_1