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正弦和余弦函数的垂直伸缩

正弦和余弦函数的垂直伸缩
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2019-02-15 22:37
函数三角函数函数图像
①本范例演示了正弦和余弦函数图像在垂直方向上的伸缩变换现象；②涉及的核心数学概念包括函数图像变换、正弦函数、余弦函数、垂直伸缩系数；③作图要点——从下方『构造摘要』提炼用到了UnicodeToLetter, Polygon, LaTeX, Segment, Translate等GeoGebra命令/对象；④适合高中阶段学习三角函数变换的学生或教师使用。

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(("a=" * a)) → lblA
  5. LaTeX((("g(x)=" * a) * "\cos(x°)")) → lblACos
  6. LaTeX((("g(x)=" * a) * "\sin(x°)")) → lblASin
  7. LaTeX("f(x)=\cos(x°)") → lblCos
  8. LaTeX("f(x)=\sin(x°)") → lblSin
  9. LaTeX("\text{\textbf{Question: }Given \(f(x)\) and \(g(x)=af(x)\), how do the properties of \(g(x)\) change as \\the value of \(a\) changes? Consider amplitude, period, equation of the axis, and range. }") → MainInstruc
  10. LaTeX("\text{\textbf{Instructions: }Move the slider and observe the changes to the graph of \(g(x)\).\\Click `Try Another' to experiment with a different function. ") → SpecInstruc
  11. Segment(legendAnchor1, legendAnchor1 + (90, 0)) → legendSegment1
  12. Translate(legendSegment1, Vector[(0, 0), (0, -2.3)]) → legendSegment2