30n°角的正弦与余弦几何构造与数值演示

30n°角的正弦与余弦几何构造与数值演示
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2016-10-01 12:41
本范例演示了 30 度整数倍角(30n°)的正弦与余弦值在单位圆上的几何分布规律。核心数学概念涵盖三角函数定义、角度序列及反射变换。作图要点包括使用 Circle 构建单位圆,利用 Mirror 和 Segment 绘制对应线段,通过 Polygon 和 Angle 展示角度关系,并结合 Point 与 Intersect 确定坐标点。该工具适合高中学生理解三角函数周期性,或教师用于课堂动态演示,帮助直观掌握特殊角的三角函数值。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Intersect(c, f, 1) → C
  5. Intersect(c, f, 2) → D
  6. Intersect(c, g, 2) → E
  7. Intersect(c, g, 1) → F
  8. Mirror(E, xAxis) → E'
  9. Mirror(F, xAxis) → F'
  10. Mirror(C, yAxis) → C'
  11. Mirror(D, yAxis) → D'
  12. Intersect(c, xAxis, 2) → G
  13. Intersect(c, yAxis, 2) → H
  14. Intersect(c, yAxis, 1) → I
  15. Segment(A, E) → j
  16. Segment(A, E') → k
  17. Segment(E, E') → l
  18. Polygon(A, C', C) → poly2, n, p, q
  19. Polygon(A, E', E) → poly1, e, a, e'
  20. Segment(G, C') → m
  21. Polygon(A, F, F') → poly4, f', a_3, f_1
  22. Polygon(D, D', A) → poly5, r, s, t
  23. Segment(A, B) → b
  24. Segment(A, H) → d
  25. Segment(G, A) → g_1
  26. Segment(A, I) → h_1
  27. Intersect(i, l) → J
  28. Segment(A, J) → i_1
  29. Angle(E, J, A) → α
  30. Intersect(h, p) → K
  31. Segment(K, A) → j_1
  32. Angle(C', K, A) → β
  33. Intersect(i, a_3) → L
  34. Segment(L, A) → k_1
  35. Angle(F', L, A) → γ
  36. Intersect(h, r) → M
  37. Segment(A, M) → l_1
  38. Angle(D, M, A) → δ
  39. Polygon(P, N, O, Q) → poly3, p_1, n_1, o, q_1
  40. Polygon(P_1, N_1, O_1, Q_1) → poly3_1, p_2, n_2, o_1, q_2
  41. Polygon(P_2, N_2, O_2, Q_2) → poly3_2, p_3, n_3, o_2, q_3
  42. Polygon(P_3, N_3, O_3, Q_3) → poly3_3, p_4, n_4, o_3, q_4
  43. Polygon(P_4, N_4, O_4, Q_4) → poly3_4, p_5, n_5, o_4, q_5
  44. Polygon(P_5, N_5, O_5, Q_5) → poly3_5, p_6, n_6, o_5, q_6
  45. Polygon(P_6, N_6, O_6, Q_6) → poly3_6, p_7, n_7, o_6, q_7
  46. Polygon(P_7, N_7, O_7, Q_7) → poly3_7, p_8, n_8, o_7, q_8
  47. Polygon(P_8, N_8, O_8, Q_8) → poly3_8, p_9, n_9, o_8, q_9
  48. Polygon(P_9, N_9, O_9, Q_9) → poly3_9, p_{10}, n_{10}, o_9, q_{10}
  49. Polygon(P_{10}, N_{10}, O_{10}, Q_{10}) → poly3_{10}, p_{11}, n_{11}, o_{10}, q_{11}
  50. Polygon(P_{11}, N_{11}, O_{11}, Q_{11}) → poly3_{11}, p_{12}, n_{12}, o_{11}, q_{12}