Intuitive Derivative of the Sin Function

GeoGebra Commands & Parameters

1. Point(f) → E
2. Point(f) → F
3. Point(f) → G
4. Point(f) → H
5. Segment((x(A) - d, y(A)), (x(A) + d, y(A))) → A_s
6. Rotate(A_s, atand(m_1), A) → A_s'
7. Slope(A_s') → m
8. Segment((x(B) - d, y(B)), (x(B) + d, y(B))) → B_s
9. Rotate(B_s, atand(m_2), B) → B_s'
10. Point(A_s') → I
11. OrthogonalLine(I, xAxis) → i
12. Point(A_s') → J
13. OrthogonalLine(J, xAxis) → j
14. OrthogonalLine(J, j) → k
15. Intersect(i, k) → K
16. Vector(I, K) → u
17. Vector(K, J) → w
18. Dilate(w, If[1 < a ≤ 2, a - 1, 0]) → v1_x
19. Dilate(u, If[0 ≤ a ≤ 1, a, 1]) → v1_y
20. Segment((x(C) - d, y(C)), (x(C) + d, y(C))) → C_s
21. Segment((x(D) - d, y(D)), (x(D) + d, y(D))) → D_s
22. Rotate(C_s, atand(m_3), C) → C_s'
23. Rotate(D_s, atand(m_4), D) → D_s'
24. Pendiente2(B, m_2, d, a) → v2_y, v2_x
25. Pendiente2(C, m_3, d, a) → v3_y, v3_x
26. Pendiente2(D, m_4, d, a) → v4_y, v4_x
27. Segment(A, A_m) → l
28. Segment(B, B_m) → n
29. Segment(C, C_m) → q
30. Segment(D, D_m) → r
31. Vector(A_0, A_m) → showAN
32. Vector(A_0, A_m) → showAP
33. Derivative(f) → f'
34. Vector(B_0, B_m) → showBP
35. Vector(B_0, B_m) → showBN
36. Vector(C_0, C_m) → showCN
37. Vector(C_0, C_m) → showCP
38. Vector(D_0, D_m) → showDN
39. Vector(D_0, D_m) → showDP
40. Segment((x(E) - d, y(E)), (x(E) + d, y(E))) → E_s
41. Segment((x(F) - d, y(F)), (x(F) + d, y(F))) → F_s
42. Segment((x(G) - d, y(G)), (x(G) + d, y(G))) → G_s
43. Segment((x(H) - d, y(H)), (x(H) + d, y(H))) → H_s
44. Rotate(E_s, atand(m_5), E) → E_s'
45. Rotate(F_s, atand(m_6), F) → F_s'
46. Rotate(G_s, atand(m_7), G) → G_s'
47. Rotate(H_s, atand(m_8), H) → H_s'
48. Vector(E_0, E_m) → showEP
49. Vector(E_0, E_m) → showEN
50. Vector(F_0, F_m) → showFN
51. Vector(G_0, G_m) → showGN
52. Vector(G_0, G_m) → showGP
53. Vector(H_0, H_m) → showHP
54. Vector(H_0, H_m) → showHN
55. Vector(F_0, F_m) → showFP