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三角函数图像绘制

三角函数图像绘制
几何画板及绘图内容加载中，请稍等……
2015-06-15 08:42
函数三角函数解析几何几何作图函数图像
①本范例演示了如何使用 GeoGebra 绘制三角函数的图像；②涉及的核心数学概念包括三角函数、函数图像、解析几何；③作图要点——从下方『构造摘要』提炼用到了 Intersect（相交）、Point（点）、Circle（圆）、Segment（线段）、Angle（角）、OrthogonalLine（垂线）、CircleArc（圆弧）、Function（函数）、Line（直线）、Polygon（多边形）、Mirror（镜像）等 GeoGebra 命令/对象；④适合的学段或用途——本范例适合高中阶段学生学习三角函数图像的绘制，有助于理解函数图像的几何性质和变换。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → b
  6. Angle(B, A, C) → θ
  7. Intersect(c, xAxis, 2) → E
  8. Segment(E, B) → a
  9. OrthogonalLine(C, a) → d
  10. Intersect(d, a) → D
  11. Segment(A, D) → e
  12. Segment(C, D) → f
  13. Point(xAxis) → F
  14. Point(xAxis) → G
  15. Segment(F, G) → g
  16. Segment(H, I) → h
  17. CircleArc(A, B, C) → k
  18. OrthogonalLine(P, g) → i
  19. Intersect(g, i) → J
  20. Segment(P, J) → j
  21. Segment(F, J) → l
  22. Function(sin(x - 2), 2, 8.3) → f_1
  23. Intersect(f_1, g, (5.14159265360225, -1.2456579871614342E-11)) → K
  24. Intersect(f_1, g, (8.283185307179632, 4.594034846457704E-14)) → L
  25. Segment(C, P) → m
  26. Point(h) → M
  27. Point(h) → N
  28. Point(yAxis) → O
  29. Point(yAxis) → Q
  30. Segment(O, Q) → n
  31. Segment(R, S) → p
  32. OrthogonalLine(T, n) → q
  33. Intersect(q, n) → U
  34. Segment(T, U) → r
  35. Segment(U, O) → s
  36. Segment(D, T) → t
  37. Point(n) → V
  38. Point(n) → W
  39. Point(n) → Y
  40. Point(n) → Z
  41. Point(p) → A_1
  42. Point(p) → B_1
  43. Segment(C_1, D_1) → a_1
  44. Segment(E_1, F_1) → b_1
  45. Point(g) → G_1
  46. Point(g) → H_1
  47. OrthogonalLine(G_1, b_1) → c_1
  48. OrthogonalLine(H_1, b_1) → d_1
  49. Intersect(b_1, c_1) → I_1
  50. Intersect(b_1, d_1) → J_1
  51. Point(c_1) → K_1
  52. Point(d_1) → L_1
  53. Segment(K_1, I_1) → e_1
  54. Segment(J_1, L_1) → g_1
  55. Point(b_1) → M_1
  56. Point(b_1) → N_1
  57. Point(b_1) → O_1
  58. Point(b_1) → P_1
  59. Point(b_1) → Q_1
  60. Point(b_1) → R_1
  61. Point(a_1) → S_1
  62. Point(a_1) → T_1
  63. Segment(I_1, U_1) → h_1
  64. Segment(W_1, J_1) → i_1
  65. OrthogonalLine(V_1, b_1) → j_1
  66. Intersect(j_1, b_1) → Y_1
  67. Segment(E_1, Y_1) → k_1
  68. Segment(A, Z_1) → l_1
  69. OrthogonalLine(Z_1, l_1) → m_1
  70. Line(A, C) → n_1
  71. Intersect(m_1, n_1) → A_2
  72. Segment(Z_1, A_2) → p_1
  73. Segment(Z_1, A_2) → q_1
  74. Segment(A, A_2) → r_1
  75. Segment(A_2, V_1) → s_1
  76. Segment(V_1, Y_1) → t_1
  77. Segment(A, B_2) → a_2
  78. Segment(C, D) → b_2
  79. Polygon(N, C_2, D_2, M) → poly1, n_2, c_2, d_2, m_2
  80. Intersect(g, h) → G_2
  81. Intersect(h, m_2) → H_2
  82. Polygon(B_1, I_2, J_2, A_1) → poly2, b_3, i_2, j_2, a_3
  83. Point(a_1) → L_2
  84. Point(a_1) → M_2
  85. Mirror(I_1, a_1) → N_2
  86. Segment(O_2, P_2) → e_2
  87. Polygon(O_2, K_1, U_1, P_2) → poly3, o_2, k_2, u_1, p_2