三角函数图像研究

GeoGebra 命令及参数

1. If(angledegree, lowerlimit_d * π / 180, lowerlimit_r) → lowerlimit
2. If(angledegree, upperlimit_d / 180, upperlimit_r) → upperlimit
3. Function(g_{hidden}, lowerlimit * π, upperlimit * π) → 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 * π, upperlimit * π) → 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 + "°", (π / 180 * i - 0.05, -0.3)], i, 0, 1080, 90) → listxaxisdegreesby90
18. If(fchecktanfunction1 ≟ false, (y(Max[f, lowerlimit * π, upperlimit * π * 10]) + y(Min[f, lowerlimit * π, upperlimit * π * 10])) / 2, meanline_{1fortan}) → meanline_1
19. If(gchecktanfunction2 ≟ false, (y(Max[g, lowerlimit * π, upperlimit * π * 10]) + y(Min[g, lowerlimit * π, upperlimit * π * 10])) / 2, meanline_{2fortan}) → meanline_2
20. Textfield(h_{hidden}) → inputBox5
21. Function(h_{hidden}, lowerlimit * π, upperlimit * π) → h
22. Function(meanline_1, lowerlimit * π, upperlimit * π) → f_{meanline1}
23. Function(meanline_2, lowerlimit * π, upperlimit * π) → g_{meanline2}
24. Textfield(lowerlimit_d) → inputBox6
25. Textfield(upperlimit_d) → inputBox7
26. Function(0, lowerlimit * π, upperlimit * π + 1) → h_{x-axis}
27. Textfield(upperlimit_r) → inputBox3
28. Textfield(lowerlimit_r) → inputBox2
29. Sequence(Text[FractionText[i] + "π", (π * i - 0.15, -0.1), true, true], i, lowerlimit + xunitdistance, upperlimit, xunitdistance) → listxaxisradianlabel
30. Textfield(xaxisnumdivquad) → inputBox8
31. Sequence((i, 0), i, lowerlimit * π, upperlimit * π, xunitdistance * π) → listxaxisticks
32. Sequence(abs(f(i)), i, lowerlimit * π, upperlimit * π, 0.01) → valuestanfunction
33. Asymptote(f) → list5
34. Asymptote(Function[g, lowerlimit * π, upperlimit * π]) → list6
35. If(fchecktanfunction1 ≟ false, y(Max[f, lowerlimit * π, upperlimit * π * 10]), 0) → maxline_1
36. If(fchecktanfunction1 ≟ false, y(Min[f, lowerlimit * π, upperlimit * π * 10]), 0) → minline_1
37. Function(maxline_1, lowerlimit * π, upperlimit * π) → f_{maxline1}
38. Function(minline_1, lowerlimit * π, upperlimit * π) → 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 * π, upperlimit * π * 10]), 0) → maxline_2
48. If(gchecktanfunction2 ≟ false, y(Min[g, lowerlimit * π, upperlimit * π * 10]), 0) → minline_2
49. Function(maxline_2, lowerlimit * π, upperlimit * π) → g_{maxline1}
50. Function(minline_2, lowerlimit * π, upperlimit * π) → 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 + "°", (π / 180 * i - 0.15, -0.55)], i, lowerlimit * 180 + 180 * xunitdistance, upperlimit * 180, 180 * xunitdistance) → listxaxisdegreesby45