正弦与余弦函数的变换作图

GeoGebra 命令及参数

1. Sequence(Sequence[(i, j), i, -45, 735, 15], j, -5, 5, 0.5) → gridSpace
2. If(isSinFunc, sin(x°), cos(x°)) → parentFunc
3. Point(Union[gridSpace, {Element[homeBase, 5]}]) → B6
4. Point(Union[gridSpace, {Element[homeBase, 4]}]) → B5
5. Point(Union[gridSpace, {Element[homeBase, 3]}]) → B4
6. Point(Union[gridSpace, {Element[homeBase, 2]}]) → B3
7. Point(Union[gridSpace, {Element[homeBase, 1]}]) → B2
8. Shuffle(F2:F13) → aVals
9. Element(aVals, 1) → aVal
10. Shuffle(D2:D8) → bVals
11. Element(bVals, 1) → bVal
12. UnicodeToLetter(10003) → cmark
13. UnicodeToLetter(10007) → xmark
14. LaTeX(FractionText[abs(bVal)]) → fmtAbsBval
15. NumToFracNoPhantom(1 / abs(bVal)) → currentStretchFactor
16. LaTeX(If[isSinFunc, "y=\sin(x°)", "y=\cos(x°)"]) → lblParent
17. NumToFrac(bVal) → latexBval
18. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
19. Point(Union[gridSpace, homeBase]) → activePt
20. LaTeX((((("\text{\(y=" * NumToFrac[aVal]) * If[isSinFunc, "\sin(", "\cos("]) * NumToFrac[bVal]) * "x°)\)}")) → lblFx
21. Sequence(startXPos + (i * quarterPeriod), i, 0, 4) → correctXvals
22. LaTeX(If[bVal > 0, "", "\text{Since \(b \lt 0\), there is a reflection\\in the \(y\)-axis.}"]) → fbHReflection
23. LaTeX((((("\text{There is a horizontal stretch by a factor \\of \(" * currentStretchFactor) * "\), and the graph has the same \\\(y\)-intercept as \(") * lblParent) * "\).}")) → fbHStretch
24. If(showFeedback, E21:E22, {"", ""}) → questionMarks
25. LaTeX((((((("\text{Since \(b =" * latexBval) * "\), the period is \\\(\dfrac{360}{\mid b \mid} °=\dfrac{360}{") * fmtAbsBval) * "}°=") * abs(periodValue)) * "^\circ\).}")) → fbPeriod
26. LaTeX((("\text{The base function is \(" * lblParent) * "\)}.")) → fbBase
27. Textfield(C22) → B22
28. If(D22 ≟ periodValue, correct, incorrect) → E22
29. If(isSinFunc, (aVal * sin(((bVal * x))°)), (aVal * cos(((bVal * x))°))) → translatedFunc
30. Zip((A, translatedFunc(A)), A, correctXvals) → correctPts
31. Textfield(C21) → B21
32. If(amplitudeCorrect, correct, incorrect) → E21
33. LaTeX((((("\text{The amplitude is \(\left\vert a \right\vert = \left\vert " * NumToFracNoPhantom[aVal]) * "\right\vert = ") * NumToFracNoPhantom[abs(aVal)]) * "\)}")) → fbAmplitude
34. LaTeX(If[aVal > 0, "", "\text{Since \(a<0\), there is a reflection\\in the \(x\)-axis.}"]) → fbVReflection
35. LaTeX(If[isCorrect, "\text{The points you graphed are correct.}", "\text{You did not graph a correct set of points.}"]) → fbCorrect
36. LaTeX(If[bVal < 0, "\text{Note that this reflection has no effect for a\\cosine function, since the cosine function\\is symmetric about the \(y-\)axis.}", ""]) → fbCosReflection
37. LaTeX(If[aVal < 0 ∧ bVal < 0, "\text{Note that for a sine function, the reflections \\in the \(x\)-axis and the \(y-\)axis cancel\\each other out.}", If[aVal < 0 ∨ bVal < 0, (("\text{For a sine function, this reflection has the\\same effect as a reflection in the \(" * If[aVal < 0, "y", "x"]) * "\)-axis.}"), ""]]) → fbSinReflection
38. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
39. LaTeX(((((((((((fbAmplitude * "\\") * fbPeriod) * "\\") * fbBase) * "\\") * fbVReflection) * "\\") * fbHReflection) * "\\") * If[isSinFunc, fbSinReflection, fbCosReflection])) → fbAll
40. Segment(Element[legendPoints, 1], Element[legendPoints, 1] + (60, 0)) → legendParent
41. Segment(Element[legendPoints, 2], Element[legendPoints, 2] + (60, 0)) → legendTransformed
42. TableText({questionLbls, questionSpacers, questionMarks}, "vr") → tblInput