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单位圆探索 by Amanda Vanus

单位圆探索 by Amanda Vanus
几何画板及绘图内容加载中，请稍等……
2018-02-02 01:06
圆函数三角函数解析几何几何作图
①本范例演示单位圆与三角函数的关系，通过动态作图揭示角度、坐标与三角函数值的对应；②涉及核心数学概念包括单位圆、三角函数、解析几何、几何变换；③作图要点运用了点、垂线、线段、距离测量等 GeoGebra 命令，以及对象 A, B, f, D, g, h, distanceAD 等；④适合高中数学教学，用于帮助学生直观理解三角函数定义及几何意义。

GeoGebra 命令及参数

  1. Point(xAxis) → B
  2. OrthogonalLine(B, xAxis) → f
  3. Point(f) → D
  4. Segment(A, B) → g
  5. Segment(A, D) → h
  6. Distance(A, D) → distanceAD
  7. Segment(D, B) → i
  8. Point(xAxis) → E
  9. OrthogonalLine(E, xAxis) → j
  10. Point(j) → F
  11. Segment(F, E) → k
  12. Segment(F, A) → l
  13. Distance(F, A) → distanceFA
  14. Segment(E, A) → m
  15. Point(xAxis) → G
  16. OrthogonalLine(G, xAxis) → n
  17. Point(n) → H
  18. Segment(H, A) → p
  19. Segment(H, G) → q
  20. Segment(G, A) → r
  21. Distance(H, A) → distanceHA
  22. Distance(G, A) → distanceGA
  23. Point(xAxis) → I
  24. OrthogonalLine(I, xAxis) → s
  25. Point(s) → J
  26. Segment(A, I) → b
  27. Segment(I, J) → c
  28. Distance(J, A) → distanceJA
  29. Segment(J, A) → t
  30. Distance(J, A) → d
  31. Point(xAxis) → C
  32. OrthogonalLine(C, xAxis) → e
  33. Point(e) → K
  34. Segment(K, C) → g_1
  35. Segment(C, A) → h_1
  36. Segment(A, K) → f_1
  37. Distance(A, K) → distanceAK
  38. Point(xAxis) → L
  39. OrthogonalLine(L, xAxis) → i_1
  40. Point(i_1) → M
  41. Segment(A, M) → j_1
  42. Segment(M, L) → k_1
  43. Segment(L, A) → l_1
  44. Distance(A, M) → distanceAM
  45. Point(xAxis) → N
  46. OrthogonalLine(N, xAxis) → m_1
  47. Point(m_1) → O
  48. Segment(A, O) → n_1
  49. Segment(O, N) → p_1
  50. Segment(N, A) → q_1
  51. Distance(A, O) → distanceAO
  52. Point(xAxis) → P
  53. OrthogonalLine(P, xAxis) → r_1
  54. Point(r_1) → Q
  55. Segment(A, Q) → s_1
  56. Segment(Q, P) → t_1
  57. Segment(P, A) → a_1
  58. Distance(Q, A) → distanceQA
  59. Point(xAxis) → R
  60. OrthogonalLine(R, xAxis) → b_1
  61. Point(b_1) → S
  62. Segment(R, S) → c_1
  63. Segment(S, A) → d_1
  64. Segment(A, R) → e_1
  65. Distance(A, S) → distanceAS
  66. Point(xAxis) → T
  67. OrthogonalLine(T, xAxis) → f_2
  68. Point(f_2) → U
  69. Segment(A, U) → g_2
  70. Segment(T, U) → h_2
  71. Segment(T, A) → i_2
  72. Distance(A, U) → distanceAU
  73. Point(xAxis) → V
  74. OrthogonalLine(V, xAxis) → j_2
  75. Point(j_2) → W
  76. Segment(A, W) → k_2
  77. Segment(W, V) → l_2
  78. Segment(V, A) → m_2
  79. Distance(A, W) → distanceAW
  80. Point(xAxis) → Z
  81. OrthogonalLine(Z, xAxis) → n_2
  82. Point(n_2) → A_1
  83. Segment(A, A_1) → p_2
  84. Segment(A_1, Z) → q_2
  85. Distance(A_1, A) → distanceA1A
  86. Segment(Z, A) → r_2
  87. Point(l_1) → B_1
  88. OrthogonalLine(B_1, l_1) → s_2
  89. Point(s_2) → C_1
  90. Segment(B_1, C_1) → t_2
  91. Segment(C_1, A) → a_2
  92. Segment(A, B_1) → b_2
  93. Distance(A, C_1) → distanceAC1

AI 绘图提示语参考

画一个单位圆，并在圆上标记点，从圆心向x轴作垂线，垂足为点B，过B点作垂线交圆于点D，连接圆心和D点，再从圆心作x轴的垂线交圆于另一点，连接圆心和该点，分别测量两点到圆心的距离，并画出这两条线段。
以上提示语为根据原始绘图命令整理而来，仅供参考。