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正弦函数平移变换演示

正弦函数平移变换演示
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2019-02-21 00:16
函数三角函数函数图像
①本范例演示正弦函数图像的平移变换现象；②涉及核心数学概念包括函数图像平移、正弦函数特性、参数变换影响；③作图要点提炼自构造摘要，使用了GeoGebra命令/对象：UnicodeToLetter, Polygon, LaTeX, Segment, Translate, 对象包括HowDidIDo, TryAnother, xmark, cmark, incorrect, correct, isDone, bottomLeft, topLeft, viewbox, showFeedback, h, cos_1, isSinFunc, sin_1, lblCos, lblSin, MainInstruc, lblH, k, lblK, sin_2, cos_2, lblSin_2, lblCos_2, SpecInstruc, legendAnchor1, legendSegment1, legendSegment2；④适合高中数学教学，用于理解函数图像变换规律及参数k、h的意义。

GeoGebra 命令及参数

  1. UnicodeToLetter(10007) → xmark
  2. UnicodeToLetter(10003) → cmark
  3. Polygon({bottomLeft, (x(bottomLeft), y(topLeft)), topLeft, (x(topLeft), y(bottomLeft))}) → viewbox
  4. LaTeX("f(x)=\cos(x°)") → lblCos
  5. LaTeX("f(x)=\sin(x°)") → lblSin
  6. LaTeX("\text{\textbf{Question: }Given \(g(x)=f(x-h)+k\), how do the characteristics of \(g(x)\) change as \\the values of \(h\) and \(k\) change? Consider amplitude, period, equation of the axis, and range. }") → MainInstruc
  7. LaTeX((("h=" * h) * "^\circ")) → lblH
  8. LaTeX(("k = " * k)) → lblK
  9. LaTeX(("g(x)=" * sin_2)) → lblSin_2
  10. LaTeX(("g(x)=" * cos_2)) → lblCos_2
  11. LaTeX("\text{\textbf{Instructions: }Move the sliders and observe the changes to the graph of \(g(x)\).\\Click `Try Another' to experiment with a different function. ") → SpecInstruc
  12. Segment(legendAnchor1, legendAnchor1 + (90, 0)) → legendSegment1
  13. Translate(legendSegment1, (0, -2)) → legendSegment2