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Vertical Stretches of Sine and Cosine Functions

Vertical Stretches of Sine and Cosine Functions
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2019-02-15 22:37
FunctionTrigonometryGraphing
This example demonstrates the vertical stretch transformations of sine and cosine function graphs. It involves core math concepts like function graph transformations, sine and cosine functions, and vertical stretch coefficients. GeoGebra commands/objects used include UnicodeToLetter, Polygon, LaTeX, Segment, Translate. Suitable for high school students or teachers learning trigonometric function transformations.

GeoGebra Commands & Parameters

  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