三角函数图像自学交互工具

GeoGebra 命令及参数

1. If(angledegree, (lowerlimit_d * pi / 180), lowerlimit_r) → lowerlimit
2. If(angledegree, upperlimit_d / 180, upperlimit_r) → upperlimit
3. Function(g_{hidden}, (lowerlimit * pi), (upperlimit * pi)) → g
4. Derivative(g_{hidden}) → g'
5. RemoveUndefined(Sequence[x(Root[g', i]), i, -31.41593, 31.41593, 0.31416]) → sincosturningptslistg
6. Function(f_{hidden}, (lowerlimit * pi), (upperlimit * pi)) → f
7. Derivative(f_{hidden}) → f'
8. RemoveUndefined(Sequence[x(Root[f', i]), i, -31.41593, 31.41593, 0.31416]) → sincosturningptslistf
9. Point(g) → P_{02}
10. Point(f) → P_{01}
11. If(Length[sincosturningptslistg] > 0, false, true) → gchecktanfunction2
12. Derivative(g') → g''
13. Derivative(f') → f''
14. If(Length[sincosturningptslistf] > 0, false, true) → fchecktanfunction1
15. Textfield(f_{hidden}) → inputBox1
16. Textfield(g_{hidden}) → inputBox4
17. Sequence(Text[i + "°", ((pi / 180 * i) - 0.05, -0.3)], i, 0, 1080, 90) → listxaxisdegreesby90
18. If(fchecktanfunction1 ≟ false, (y(Max[f, (lowerlimit * pi), ((upperlimit * pi) * 10)]) + y(Min[f, (lowerlimit * pi), ((upperlimit * pi) * 10)])) / 2, meanline_{1fortan}) → meanline_1
19. If(gchecktanfunction2 ≟ false, (y(Max[g, (lowerlimit * pi), ((upperlimit * pi) * 10)]) + y(Min[g, (lowerlimit * pi), ((upperlimit * pi) * 10)])) / 2, meanline_{2fortan}) → meanline_2
20. Textfield(h_{hidden}) → inputBox5
21. Function(h_{hidden}, (lowerlimit * pi), (upperlimit * pi)) → h
22. Function(meanline_1, (lowerlimit * pi), (upperlimit * pi)) → f_{meanline1}
23. Function(meanline_2, (lowerlimit * pi), (upperlimit * pi)) → g_{meanline2}
24. Textfield(lowerlimit_d) → inputBox6
25. Textfield(upperlimit_d) → inputBox7
26. Function(0, (lowerlimit * pi), (upperlimit * pi) + 1) → h_{x-axis}
27. Textfield(upperlimit_r) → inputBox3
28. Textfield(lowerlimit_r) → inputBox2
29. Sequence(Text[FractionText[i] + "π", ((pi * i) - 0.15, -0.1), true, true], i, lowerlimit + xunitdistance, upperlimit, xunitdistance) → listxaxisradianlabel
30. Textfield(xaxisnumdivquad) → inputBox8
31. Sequence((i, 0), i, (lowerlimit * pi), (upperlimit * pi), (xunitdistance * pi)) → listxaxisticks
32. Sequence(abs(f(i)), i, (lowerlimit * pi), (upperlimit * pi), 0.01) → valuestanfunction, {2, 1.999400019999733, 1.9976003199829337, 1.9946016198056125, 1.9904051189078582, 1.9850124958340776, 1.9784259075615989, 1.9706479886379116, 1.961681850126881, 1.9515310783643645, 1.940199733523725, 1.9276923479918167, 1.9140139245560892, 1.8991699344035395, 1.8831663149323132, 1.8660094673768182, 1.8477062542473224, 1.8282639965850387, 1.8076904710338044, 1.785993906729531, 1.7631829820086553, 1.7392668209369249, 1.71425498965989, 1.6881574925765754, 1.6609847683378525, 1.6327476856711178, 1.6034575390329495, 1.573126044091472, 1.541765333040248, 1.5093879497455607, 1.4760068447290347, 1.4416353699876012, 1.406287273652877, 1.3699766944920948, 1.3327181562527834, 1.294526561853465, 1.2554171874226845, 1.2154056761887633, 1.174508032222715, 1.1327406140368312, 1.0901201280414954, 1.04666362186284, 1.0023884775239233, 0.9573124044921548, 0.9114534325957395, 0.8648299048119923, 0.8174604699303873, 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33. Asymptote(f) → list5
34. Asymptote(Function[g, (lowerlimit * pi), (upperlimit * pi)]) → list6
35. If(fchecktanfunction1 ≟ false, y(Max[f, (lowerlimit * pi), ((upperlimit * pi) * 10)]), 0) → maxline_1
36. If(fchecktanfunction1 ≟ false, y(Min[f, (lowerlimit * pi), ((upperlimit * pi) * 10)]), 0) → minline_1
37. Function(maxline_1, (lowerlimit * pi), (upperlimit * pi)) → f_{maxline1}
38. Function(minline_1, (lowerlimit * pi), (upperlimit * pi)) → f_{minline1}
39. Intersect(f_{maxline1}, vertline1) → A_1
40. Intersect(f_{minline1}, vertline1) → B_1
41. Intersect(f_{meanline1}, vertline1) → C_1
42. Distance(A_1, C_1) → distanceA1C1
43. Vector(C_1, A_1) → u_1
44. Vector(C_1, B_1) → v_1
45. Midpoint(A_1, C_1) → M_{A1C1}
46. Midpoint(B_1, C_1) → M_{C1B1}
47. If(gchecktanfunction2 ≟ false, y(Max[g, (lowerlimit * pi), ((upperlimit * pi) * 10)]), 0) → maxline_2
48. If(gchecktanfunction2 ≟ false, y(Min[g, (lowerlimit * pi), ((upperlimit * pi) * 10)]), 0) → minline_2
49. Function(maxline_2, (lowerlimit * pi), (upperlimit * pi)) → g_{maxline1}
50. Function(minline_2, (lowerlimit * pi), (upperlimit * pi)) → g_{minline1}
51. Intersect(g_{maxline1}, vertline2) → A_2
52. Intersect(g_{minline1}, vertline2) → B_2
53. Intersect(g_{meanline2}, vertline2) → C_2
54. Midpoint(A_2, C_2) → M_{A2C2}
55. Midpoint(B_2, C_2) → M_{B2C2}
56. Distance(A_2, C_2) → distanceAC
57. Vector(C_2, A_2) → u_2
58. Vector(C_2, B_2) → v_2
59. If(fchecktanfunction1, tancyclesf, sincoscycles1) → cycles1
60. If(gchecktanfunction2, tancyclesg, sincoscycles2) → cycles2
61. Intersect(g, vertline3, (0, -1.5)) → P_1
62. Midpoint(P_1, Q_1) → M_{P1Q1}
63. Vector(M_{P1Q1}, P_1) → u_{p1l}
64. Vector(M_{P1Q1}, Q_1) → u_{p1r}
65. Intersect(f, vertline4, (0.08997312945277669, 1.9515599378378266)) → P_2
66. Midpoint(P_2, Q_2) → M_{P2Q2}
67. Vector(M_{P2Q2}, Q_2) → u_{p2r}
68. Vector(M_{P2Q2}, P_2) → u_{p2l}
69. Derivative(f'') → f'''
70. Derivative(g'') → g'''
71. Sequence(Text[i + "°", ((pi / 180 * i) - 0.15, -0.55)], i, (lowerlimit * 180) + (180 * xunitdistance), (upperlimit * 180), (180 * xunitdistance)) → listxaxisdegreesby45