Trigonometric Functions on the Unit Circle by Sete Cordas

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A_2
2. Circle(A_2, 1) → c
3. Point(c) → A
4. Segment(A_2, A) → r
5. Line(A, xAxis) → g
6. OrthogonalLine(A, xAxis) → h
7. Intersect(h, xAxis) → C
8. Segment(A_2, C) → i
9. Segment(C, A) → rsinθ
10. OrthogonalLine(A, r) → l
11. Intersect(l, yAxis) → D
12. Intersect(l, xAxis) → E
13. Segment(A_2, E) → m
14. Segment(A_2, D) → n
15. Segment(E, D) → p
16. Angle(C, A_2, A) → θ
17. OrthogonalLine(A, n) → q
18. Segment(A, E) → rtanθ
19. Segment(A, D) → rcotanθ
20. Intersect(q, n) → F
21. Segment(A, F) → rcosθ
22. PointIn(c) → Pointc
23. Intersect(rsinθ, m) → G
24. Intersect(c, m, 1) → H
25. Segment(G, H) → rversinθ
26. Segment(H, E) → rexsecθ
27. Intersect(c, n, 1) → I
28. Segment(I, D) → rexcscθ
29. Segment(I, F) → rcoversθ
30. OrthogonalLine(E, g) → f
31. Point(f) → J
32. OrthogonalLine(J, f) → j
33. Intersect(j, yAxis) → K
34. Segment(J, K) → rsecθ
35. Vector(K, J) → u
36. Vector(J, K) → v
37. Line(D, xAxis) → k
38. Point(k) → L
39. OrthogonalLine(L, k) → n_1
40. Intersect(n_1, xAxis) → M
41. Vector(L, M) → w
42. Vector(M, L) → a
43. Segment(L, M) → rcscθ
44. Intersect(rcosθ, rcoversθ) → N
45. Intersect(r, i) → O
46. Segment(O, N) → s
47. OrthogonalLine(P, rcosθ) → t
48. OrthogonalLine(Q, yAxis) → b
49. Segment(F, Q) → rcovercosθ
50. Point(b) → R
51. OrthogonalLine(R, rcosθ) → d
52. Intersect(g, d) → S
53. Vector(R, S) → e
54. Vector(S, R) → u_1
55. Intersect(c, xAxis, 1) → T
56. OrthogonalLine(T, xAxis) → f_1
57. Point(f_1) → U
58. Line(U, xAxis) → g_1
59. Intersect(h, g_1) → V
60. Vector(U, V) → v_1
61. Vector(V, U) → w_1
62. Segment(U, V) → rvercosθ
63. Intersect(r, i) → Z
64. Intersect(i, rsinθ) → A_1
65. Intersect(rtanθ, xAxis) → B_1
66. Line(B_1, yAxis) → h_1
67. Point(h_1) → C_1
68. Angle(C_1, B_1, A) → α
69. Angle(A, B_1, A_1) → δ
70. Point(rcosθ) → W
71. Angle(F, A, A_2) → γ
72. Angle(D, A, F) → ζ
73. Angle(A_2, A, C) → β
74. Angle(C, A, E) → ε
75. Angle(I, D, A) → ι
76. Angle(r, s) → η