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余切定律演示

余切定律演示
几何画板及绘图内容加载中，请稍等……
2015-12-02 20:57
测试改名0角三角函数几何作图
①本范例通过动态演示展示了余切定律在三角形中的应用，揭示了边长与角余切值之间的关系；②核心数学概念涉及三角函数、余切定律、三角形几何性质；③作图要点提炼自构造摘要，使用了中点、半圆、交点、圆弧、多边形、垂线、点、线段、射线、角度、文本框等 GeoGebra 命令/对象；④适合高中及以上数学学习者，用于深入理解三角函数与几何作图的结合应用。

GeoGebra 命令及参数

  1. Midpoint(Q, P) → U_1
  2. Semicircle(Q, P) → s
  3. Intersect(Ray[P, Rotate[Q, α, P]], Ray[Q, Rotate[P, (-β), Q]]) → R
  4. Intersect(s, OrthogonalLine[Q, Line[R, Q]]) → A_1, B_1
  5. Intersect(s, OrthogonalLine[P, Line[R, P]]) → W, Z
  6. CircleArc(U_1, B_1, Z) → d_1
  7. Polygon(A, B, 3) → poly1, a, b, c, C
  8. Semicircle(B, A) → d
  9. Midpoint(A, B) → D
  10. OrthogonalLine(A, c) → e
  11. Intersect(d, e, 2) → E
  12. CircleArc(D, E, B) → f
  13. Point(f) → F
  14. Segment(A, F) → g
  15. OrthogonalLine(B, g) → h
  16. OrthogonalLine(C, h) → i
  17. OrthogonalLine(A, g) → j
  18. Intersect(i, j) → G
  19. Polygon(G, A, C) → poly2, c_1, g_1, a_1
  20. Intersect(h, i) → H
  21. Polygon(B, C, H) → poly3, h_1, b_1, c_2
  22. Polygon(B, A, F) → poly4, f_1, b_2, a_2
  23. Segment(I, J) → k
  24. Ray(J, Rotate[I, -90*°, J]) → l
  25. Ray(I, Rotate[J, 30*°, I]) → m
  26. Intersect(l, m) → L
  27. Point(Segment[J, L]) → K
  28. Polygon(I, K, 3) → poly5, n, p, q, M
  29. Intersect(l, Line[M, k]) → N
  30. Intersect(Line[M, k], Line[I, l]) → O
  31. Polygon(I, J, K) → poly6, k_1, i_1, j_1
  32. Polygon(K, M, N) → poly7, n_1, k_2, m_1
  33. Polygon(I, M, O) → poly8, o, i_2, m_2
  34. Polygon(P, Q, R) → poly9, r_1, p_1, q_1
  35. OrthogonalLine(P, q_1) → t
  36. Midpoint(P, Q) → T
  37. Angle(Q, P, R) → γ_1
  38. Angle(R, Q, P) → δ
  39. Textfield(α) → InputBox1
  40. Textfield(β) → InputBox2
  41. Angle(P, R, Q) → γ
  42. Point(d_1) → S
  43. Polygon(P, S, Q) → poly10, q_2, p_2, s_1
  44. Intersect(OrthogonalLine[R, p_2], Line[S, Q]) → V
  45. Intersect(OrthogonalLine[R, q_2], Line[S, P]) → U
  46. Polygon(R, V, Q) → poly11, q_3, r_2, v
  47. Polygon(R, U, P) → poly12, p_3, r_3, c_3