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Sine/Cosine Angle Sum Proof

Sine/Cosine Angle Sum Proof
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2019-11-27 03:10
AngleTrigonometryGeometric Construction
This example demonstrates the proof of the sum of sine and cosine angles. It involves core concepts of trigonometric functions, showing the sum formula through geometric relationships of angles and circles. GeoGebra commands used include intersection, point, segment, circle, line, ray, etc. Suitable for high school mathematics education and learning, especially for trigonometric functions and geometric proofs.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, 1]) → B
  3. Segment(A, B) → f
  4. Circle(A, B) → c
  5. Intersect(c, yAxis, 2) → C
  6. Intersect(c, xAxis, 1) → D
  7. Intersect(c, yAxis, 1) → E
  8. Segment(A, D) → g
  9. Segment(A, E) → h
  10. Segment(A, C) → i
  11. Point(c) → F
  12. Segment(A, F) → j
  13. Line(F, f) → k
  14. Line(F, i) → l
  15. Intersect(k, i) → G
  16. Intersect(l, f) → H
  17. Segment(G, F) → m
  18. Segment(F, H) → n
  19. Point(f) → I
  20. Point(c) → J
  21. Ray(A, J) → p
  22. Circle(A, K) → d
  23. Intersect(d, p, 1) → L
  24. Circle(F, Segment[A, K]) → e
  25. Intersect(e, n, 1) → M
  26. Circle(M, Segment[L, K]) → q
  27. Intersect(e, q, 1) → N
  28. Ray(F, N) → r
  29. Angle(J, A, B) → α
  30. Angle(H, F, N) → β
  31. Intersect(r, xAxis) → O
  32. Intersect(p, r) → P
  33. Intersect(n, p) → Q
  34. Segment(P, A) → s
  35. Segment(P, J) → t
  36. Angle(F, A, J) → δ
  37. OrthogonalLine(P, n) → b
  38. Intersect(b, n) → R
  39. Line(P, n) → f_1
  40. Intersect(f_1, f) → S
  41. Segment(R, P) → g_1
  42. Segment(P, S) → h_1
  43. Intersect(f, n) → T
  44. Segment(F, P) → a
  45. Angle(A, S, P) → γ
  46. Angle(A, P, F) → ε
  47. Segment(G, A) → i_1
  48. Segment(A, T) → j_1
  49. Segment(A, S) → k_1
  50. Angle(F, R, P) → ζ
  51. Segment(F, R) → l_1
  52. Segment(R, T) → m_1