单位圆上的倒数三角函数几何直观与推导

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Point(yAxis) → B
3. Point(xAxis) → C
4. Circle(A, B) → c
5. Rotate(C, θ, A) → C'
6. Angle(C, A, C') → α
7. Segment(A, C') → a
8. OrthogonalLine(C', a) → b
9. Intersect(b, xAxis) → D
10. Intersect(b, yAxis) → E
11. OrthogonalLine(C', xAxis) → d
12. OrthogonalLine(C', yAxis) → e
13. Point(yAxis) → F
14. Point(xAxis) → G
15. OrthogonalLine(G, e) → f
16. OrthogonalLine(F, d) → g
17. Intersect(e, f) → H
18. Intersect(d, g) → I
19. Segment(F, I) → cosθ
20. Point(yAxis) → J
21. Point(xAxis) → K
22. OrthogonalLine(K, xAxis) → i
23. OrthogonalLine(J, f) → j
24. OrthogonalLine(E, yAxis) → k
25. OrthogonalLine(D, xAxis) → l
26. Intersect(i, k) → L
27. Segment(L, K) → cosecθ
28. Intersect(j, l) → M
29. Segment(H, G) → sinθ
30. Intersect(d, xAxis) → N
31. Segment(C', N) → p
32. Segment(J, M) → secθ
33. Segment(E, D) → r
34. OrthogonalLine(E, r) → s
35. OrthogonalLine(C', r) → t
36. OrthogonalLine(D, r) → a_1
37. Point(yAxis) → O
38. Circle(A, O) → c_1
39. Intersect(c_1, t, 2) → P
40. OrthogonalLine(P, t) → b_1
41. Intersect(s, b_1) → Q
42. Intersect(a_1, b_1) → R
43. Segment(Q, P) → cotθ
44. Segment(P, R) → tanθ
45. Polygon(A, C', N) → poly1, n, a_2, c'
46. Polygon(N, C', D) → poly2, d_1, n_1, c'_1
47. Polygon(A, C', E) → poly3, e_1, a_3, c'_2