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和角正切公式探索

和角正切公式探索
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2015-12-24 08:53
角函数三角函数
所属专题 Trigonometric Identities
本范例通过互动谜题和证明，探索两个角之和的正切公式。核心数学概念包括三角函数和和角公式。使用GeoGebra命令如Point、OrthogonalLine、Ray等进行几何作图。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(a) → A
  2. Point(b) → B
  3. OrthogonalLine(B, a) → f
  4. Point(a) → D
  5. Ray(A, D) → g
  6. Point(g) → E
  7. Segment(B, E) → h
  8. OrthogonalLine(E, b) → i
  9. Intersect(a, f) → F
  10. Segment(A, F) → j
  11. Segment(B, F) → k
  12. OrthogonalLine(E, b) → l
  13. Intersect(b, l) → H
  14. Segment(B, H) → n
  15. Angle(E, F, B) → β
  16. Segment(A, E) → s
  17. Segment(E, F) → t
  18. Point(t) → C
  19. Segment(B, C) → c
  20. OrthogonalLine(C, c) → d
  21. OrthogonalLine(E, t) → e
  22. Intersect(d, e) → G
  23. Segment(B, G) → m
  24. Segment(G, C) → p
  25. Angle(G, C, B) → α
  26. Angle(B, H, G) → γ
  27. Segment(H, E) → q
  28. Angle(F, B, C) → δ
  29. Angle(C, B, G) → ε
  30. Angle(H, G, B) → ζ
  31. Angle(E, C, G) → η
  32. Angle(H, E, F) → θ
  33. Segment(H, G) → r
  34. Segment(G, E) → a_1
  35. Segment(E, C) → b_1
  36. Segment(C, F) → c_1
  37. Distance(B, C) → distanceBC
  38. Distance(B, G) → distanceBG
  39. Angle(C, G, E) → ι
  40. Polygon(B, F, C) → poly1, c_2, b_2, f_1
  41. Polygon(C, E, G) → poly2, g_1, c_3, e_1
  42. Segment(H, B) → d_1
  43. Segment(H, G) → h_1
  44. Segment(G, E) → i_1
  45. Segment(E, C) → j_1
  46. Segment(C, F) → k_1
  47. Segment(F, B) → l_1
  48. Segment(B, C) → m_1
  49. Segment(C, G) → n_1
  50. Segment(G, B) → p_1
  51. Distance(B, F) → distanceBF