正弦函数图像绘制 by Walch Education

GeoGebra 命令及参数

1. LaTeX(steps) → counter
2. Simplify((b * x)) → argum
3. FractionText(dl) → domleft
4. FractionText(dr) → domright
5. LaTeX((domleft * "\pi")) → domLeft
6. LaTeX((domright * "\pi")) → domRight
7. LaTeX((((((("\textcolor{#000099}{f(x)=" * f) * "}\text{ over }\textcolor{#000099}{\left[") * domLeft) * ",") * domRight) * "\right]}")) → Problem
8. LaTeX("\text{Identify the amplitude of the function.}") → text1
9. LaTeX("\text{This will help determine the y-axis scale.}") → text2
10. LaTeX("\text{Determine the period of the function.}") → text4
11. LaTeX((((("\text{The sine argument is }\textcolor{#000099}{" * argum) * "}\text{. Solve }\textcolor{#000099}{") * argum) * "=2\pi}\text{ for }\textcolor{#000099}{x}\text{ to find the period.}")) → text6
12. LaTeX("\text{Identify any other coefficients or terms that would affect the shape of the graph.}") → text8
13. LaTeX("\text{This is necessary to determine if the graph is translated horizontally or vertically, or if}\cr\text{other mathematical terms affect the graph’s shape.}") → text9
14. LaTeX("\text{This will determine how many cycles of the function show in the given domain.}") → text5
15. LaTeX("\text{Draw and label the axes for your graph.}") → text12
16. LaTeX("\text{The x-axis scale is determined by the given restricted domain.}") → text13
17. LaTeX((((("\text{The x-axis scale will cover at least from }\textcolor{#000099}{" * dl) * "\pi}\text{ to }\textcolor{#000099}{") * dr) * "\pi}.")) → text14
18. LaTeX("\text{The y-axis scale is determined by the amplitude and the vertical shift, if any.}") → text15
19. LaTeX((((("\text{The y-axis scale should cover at least from }\textcolor{#000099}{y = " * Simplify[c - a]) * "}\text{ to }\textcolor{#000099}{y = ") * Simplify[c + a]) * "}.")) → text16
20. LaTeX("\text{The sine function is zero when its argument is }\textcolor{#000099}{\pm n\pi}\text{ where }\textcolor{#000099}{n}\text{ is an integer, }\textcolor{#000099}{0,1,2,\ldots}.") → text18
21. Zip(FractionText[a], a, zeros) → zerolist
22. Zip(LaTeX[(a * "\pi")], a, zerolist) → zerolistfull
23. Zip(((a * π), c), a, zeros) → zeropts
24. TableText({zerolistfull}) → zerosnq
25. LaTeX((((("\textcolor{#000099}{" * b) * "x=\pm n\pi}\cr\textcolor{#000099}{x=") * zerosnq) * "}")) → text19
26. LaTeX("\text{Determine what values of the restricted domain are the maximum and minimum of the}\cr\text{function value(s). List the points corresponding to these extremes, and plot them on the}\cr\text{graph.}") → text21
27. LaTeX("\text{The sine function has maximums when its argument is }\textcolor{#000099}{\frac{\pi}{2}\pm2n\pi}\text{ where }\textcolor{#000099}{n}\text{ is an integer.}") → text22
28. Zip(FractionText[a], a, maxes) → maxlist
29. Zip(LaTeX[(a * "\pi")], a, maxlist) → maxlistfull
30. TableText({maxlistfull}) → maxnq
31. LaTeX("\text{The sine function has minimums when its argument is }\textcolor{#000099}{-\frac{\pi}{2}\pm2n\pi}\text{ where }\textcolor{#000099}{n}\text{ is an integer.}") → text25
32. Zip(FractionText[a], a, mins) → minlist
33. Zip(LaTeX[(a * "\pi")], a, minlist) → minlistfull
34. TableText({minlistfull}) → minnq
35. Zip(((u * π), c + abs(a)), u, maxes) → maxpts
36. Zip(((u * π), c - abs(a)), u, mins) → minpts
37. LaTeX("\text{Sketch a smooth curve over the given restricted domain.}") → text46
38. LaTeX("\text{Determine the values of the restricted domain for which the sine value(s) equal 0.}\cr\text{List the points corresponding to these zeros, and plot them on the graph.}") → text17
39. LaTeX((((((((((((("\textcolor{#000099}{x=\frac{2}{" * b) * "}\pi}\text{ The period is }\textcolor{#000099}{") * permult) * "\pi}.\cr\text{The number of cycles in the domain is }\textcolor{#000099}{\frac{domain}{period}=\frac{") * domRight) * "-") * domLeft) * "}{\frac{2}{") * b) * "}\pi}=") * cycles) * ".}")) → text7
40. Zip(LaTeX[((((((((a * "\sin\left((") * b) * ")\left(") * u) * "\right)\right)+(") * c) * ")=") * y(v))], u, maxlistfull, v, maxpts) → ymaxlist
41. Zip(LaTeX[((((((((a * "\sin\left((") * b) * ")\left(") * u) * "\right)\right)+(") * c) * ")=") * y(v))], u, minlistfull, v, minpts) → yminlist
42. TableText({yminlist}, "v") → ymintext
43. TableText({ymaxlist}, "v") → ymaxtext
44. Zip(LaTeX[((((((((a * "\sin\left((") * b) * ")\left(") * u) * "\right)\right)+(") * c) * ")=") * y(v))], u, zerolistfull, v, zeropts) → yzero
45. FractionText(permult) → permulttext
46. TableText({yzero}, "v") → yzerotext
47. LaTeX("\text{Move the slider to solve the problem.}") → text0
48. LaTeX("\text{Use the buttons below to return to the original problem or}\cr\text{randomly generate a similar practice problem.}") → text47
49. LaTeX((((("\text{The coefficient of the sine function is }\textcolor{#000099}{" * a) * "}\text{; therefore, the amplitude is }\textcolor{#000099}{") * a) * "}.")) → text3
50. LaTeX("\text{The sine argument has no constant term, so there is no horizontal shift.}") → text10
51. LaTeX((("\text{The corresponding y-values are: }\textcolor{#000099}{" * yzerotext) * "}")) → text20
52. LaTeX((("\text{The y-values are: }\textcolor{#000099}{" * ymaxtext) * "}")) → text24
53. LaTeX((("\text{The corresponding y-values are: }\textcolor{#000099}{" * ymintext) * "}")) → text27
54. If(c ≟ 0, LaTeX["\text{The function has no constant term, so there is no vertical shift.}"], If[c > 0, LaTeX[(((("\text{The constant term } \textcolor{#000099}{+" * c) * "} \text{ in the function means the sine function will be shifted up by }\textcolor{#000099}{") * abs(c)) * "}.")], LaTeX[(((("\text{The constant term in the function }\textcolor{#000099}{" * c) * "}\text{ means the sine function will be shifted down by }\textcolor{#000099}{") * abs(c)) * "}.")]]) → text11
55. LaTeX((((("\textcolor{#000099}{" * b) * "x=\frac{\pi}{2}\pm 2n\pi} \to \textcolor{#000099}{x=") * maxnq) * "}")) → text23
56. LaTeX((((("\textcolor{#000099}{" * b) * "x=-\frac{\pi}{2}\pm 2n\pi } \to \textcolor{#000099}{ x=") * minnq) * "}")) → text26