Cosine and Sine of 45°

GeoGebra Commands & Parameters

1. Intersect(xAxis, yAxis) → A
2. Point(xAxis) → B
3. Circle(A, B) → c
4. Intersect(c, y = x, 2) → E
5. Intersect(c, y = (-x), 1) → F
6. Mirror(E, xAxis) → E'
7. Mirror(F, xAxis) → F'
8. Intersect(c, xAxis, 2) → G
9. Intersect(c, yAxis, 2) → H
10. Intersect(c, yAxis, 1) → I
11. Segment(A, E) → j
12. Segment(A, E') → k
13. Segment(E, E') → l
14. Polygon(A, E', E) → poly1, e, a, e'
15. Polygon(A, F, F') → poly4, f', a_3, f_1
16. Segment(A, B) → b
17. Segment(A, H) → d
18. Segment(G, A) → g_1
19. Segment(A, I) → h_1
20. Intersect(i, l) → J
21. Angle(E, J, A) → α
22. Intersect(i, a_3) → L
23. Polygon(P, N, O, Q) → poly3, p_1, n_1, o, q_1
24. Polygon(P_1, N_1, O_1, Q_1) → poly3_1, p_2, n_2, o_1, q_2
25. Polygon(P_2, N_2, O_2, Q_2) → poly3_2, p_3, n_3, o_2, q_3
26. Polygon(P_3, N_3, O_3, Q_3) → poly3_3, p_4, n_4, o_3, q_4
27. Polygon(P_4, N_4, O_4, Q_4) → poly3_4, p_5, n_5, o_4, q_5
28. Polygon(P_5, N_5, O_5, Q_5) → poly3_5, p_6, n_6, o_5, q_6
29. Polygon(P_6, N_6, O_6, Q_6) → poly3_6, p_7, n_7, o_6, q_7
30. Polygon(P_7, N_7, O_7, Q_7) → poly3_7, p_8, n_8, o_7, q_8
31. Polygon(P_9, N_9, O_9, Q_9) → poly3_9, p_{10}, n_{10}, o_9, q_{10}
32. Polygon(P_{10}, N_{10}, O_{10}, Q_{10}) → poly3_{10}, p_{11}, n_{11}, o_{10}, q_{11}
33. Polygon(P_{11}, N_{11}, O_{11}, Q_{11}) → poly3_{11}, p_{12}, n_{12}, o_{11}, q_{12}
34. Polygon(A, L, F) → poly2, f_2, a_1, l_1
35. Angle(F, L, A) → γ
36. Polygon(A, L, F') → poly5, f'_1, a_2, l_2
37. Angle(F', L, A) → β
38. Polygon(A, J, E) → poly6, e_1, a_4, j_1
39. Polygon(A, J, E) → poly7, e_2, a_5, j_2
40. Polygon(A, J, E') → poly8, e'_1, a_6, j_3
41. Angle(A, J, E') → δ