探索单位圆：动态可视化三角函数与特殊角

GeoGebra 命令及参数

1. Point(c) → A
2. Sequence(((π * k)) / 12, k, 0, 24) → Angles
3. Sequence((cos(Element[Angles306090, k]), sin(Element[Angles306090, k])), k, 1, 9) → Pts306090
4. Segment(O, B) → d
5. Min(abs(Angles306090 - acosd(x(A)))) → d306090
6. Min(abs(Angles459045 - acosd(x(A)))) → d459045
7. Min(abs(AnglesVH - acosd(x(A)))) → dVH
8. If(d306090 ≤ d459045 ∧ d306090 ≤ dVH, 1, 0) → is306090
9. If(d459045 < d306090 ∧ d459045 < dVH, 1, 0) → is459045
10. If(dVH < d306090 ∧ dVH < d459045, 1, 0) → isVH
11. If(y(A) > 0, acosd(x(A)), π + acosd((-x(A)))) → theta
12. Polygon(O, A, B) → Triangle306090, b, o, a
13. Polygon(O, A, B) → Triangle459045, b_1, o_1, a_1
14. Polygon(O, A, B) → TriangleVH, b_2, o_2, a_2
15. Sequence((cos(Element[Angles459045, k]), sin(Element[Angles459045, k])), k, 1, 4) → Pts459045
16. Sequence((cos(Element[AnglesVH, k]), sin(Element[AnglesVH, k])), k, 1, 4) → PtsVH
17. Sequence((cos(Element[AnglesAll, k]), sin(Element[AnglesAll, k])), k, 1, Length[AnglesAll]) → PtsAll
18. Element(AnglesAllLabels, 2) → Fail
19. Random(1, 14) → randInt
20. If(π / 2 < theta ∧ theta < ((3 * π)) / 2, "-", "") → negCos
21. If(tan(theta) < 0, "-", "") → negTan
22. Angle(O2, O, A) → alphaGreen
23. If(theta ≟ π / 3 ∨ theta ≟ (2 * π / 3) ∨ theta ≟ (4 * π / 3) ∨ theta ≟ (5 * π / 3), 1) → isTall306090
24. If(theta ≟ π / 6 ∨ theta ≟ (5 * π / 6) ∨ theta ≟ (7 * π / 6) ∨ theta ≟ (11 * π / 6), 1) → isSkinny306090
25. If(theta ≟ π / 4 ∨ theta ≟ (3 * π / 4) ∨ theta ≟ (5 * π / 4) ∨ theta ≟ (7 * π / 4), 1) → isReal459045
26. If(theta ≟ 0 ∨ theta ≟ π ∨ theta ≟ (2 * π), 1) → isH
27. Point(xAxis) → C
28. Point(xAxis) → D
29. Point(xAxis) → E
30. Point(xAxis) → F
31. Point(yAxis) → G
32. Point(yAxis) → H
33. Point(yAxis) → I
34. Point(yAxis) → J
35. Point(c_1) → A_1
36. Point(c_2) → A_2
37. Angle(O2, O, A) → alphaRed
38. Angle(O2, O, A) → alphaBlue
39. Point(c_3) → A_3
40. If(y(A_3) > 0, acosd(x(A_3)), π + acosd((-x(A_3)))) → theta_1
41. If(π < theta ∧ theta < (2 * π), "-", "") → negSin