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Exploring the Tangent of a Sum

Exploring the Tangent of a Sum
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2015-12-24 08:53
AngleFunctionTrigonometry
In collections Trigonometric Identities
This example uses an interactive puzzle and proof to explore the tangent of a sum of two angles. Key mathematical concepts include trigonometry and sum of angles formulas. GeoGebra commands such as Point, OrthogonalLine, and Ray are used for geometric construction. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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