相似直角三角形创建新三角函数恒等式

GeoGebra 命令及参数

1. Circle(O, 1) → c
2. Tangent(A, c) → a,
3. Segment(O, A) → e
4. Intersect(a, b) → B
5. Intersect(a, d) → C
6. OrthogonalLine(A, b) → f
7. OrthogonalLine(A, d) → g
8. Intersect(d, g) → D
9. Intersect(b, f) → E
10. Segment(A, B) → h
11. Segment(O, E) → i
12. Segment(E, A) → j
13. Segment(A, C) → k
14. Line(O, A) → l
15. Line(D, A) → m
16. Line(C, m) → n
17. Point(n) → F
18. OrthogonalLine(F, n) → p
19. Intersect(b, p) → G
20. Segment(G, F) → q
21. OrthogonalLine(B, m) → r
22. Point(d) → H
23. OrthogonalLine(H, d) → s
24. Intersect(r, s) → I
25. Segment(H, I) → t
26. Angle(A, E, O) → α
27. Intersect(l, n) → J
28. Angle(G, F, C) → γ
29. Intersect(c, yAxis, 2) → K
30. Segment(O, K) → a_1
31. Angle(t, yAxis) → δ
32. Angle(xAxis, q) → ε
33. Angle(B, I, H) → ζ
34. Angle(E, O, A) → η
35. Angle(E, A, B) → ι
36. Point(c) → L
37. Segment(O, L) → f_1
38. Intersect(n, r) → M
39. Intersect(xAxis, r) → N
40. Intersect(n, a) → P
41. Angle(P, M, N) → κ
42. Circle(O, (0.4 * i)) → c_1
43. Intersect(c_1, xAxis) → Q, R
44. Rotate(R, If[0 < u ≤ 1, ((o * π / 180) * u), (o * π / 180)], O) → R'
45. CircleSector(O, R, R') → d_1
46. Dilate(O, If[1.5 < u ≤ 2.5, 2.5 - u, 0], A) → O'
47. Vector(O, O') → v
48. Translate(d_1, v) → e_1
49. Rotate(e_1, If[2.5 < u ≤ 3.5, ((-(u - 2.5)) * π / 2), ((-π)) / 2], A) → g_1
50. Dilate(A, If[3.5 < u ≤ 4.5, 4.5 - u, 0], P) → A'
51. Vector(A, A') → w
52. Translate(g_1, w) → h_1
53. Segment(F, M) → i_1
54. Segment(N, M) → j_1
55. Segment(N, I) → k_1
56. Intersect(xAxis, q) → S