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Graphing Cosine Function

Graphing Cosine Function
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2019-02-09 03:01
FunctionTrigonometryCoordinate GeometryGraphing
This example demonstrates how to graph the cosine function using the unit circle. It involves core math concepts like cosine function, unit circle, trigonometry, and coordinate geometry. Key GeoGebra commands and objects used include Polygon, CurveCartesian, Segment, If, Sequence, and LaTeX, as extracted from the construction summary. Suitable for high school students learning trigonometric functions and coordinate geometry.

GeoGebra Commands & Parameters

  1. UnicodeToLetter(10007) → xmark
  2. UnicodeToLetter(10003) → cmark
  3. Polygon({(left, bottom), (left, top), (right, top), (right, bottom)}) → viewbox
  4. CurveCartesian((0.5 * cos(((2 * π) * t))), (0.5 * sin(((2 * π) * t))), t, If[numRevs < 0, numRevs, 0], If[numRevs < 0, 0, numRevs]) → angleCircle
  5. CurveCartesian(((0.5 * t / numRevs) * cos(((t * 2) * π))), ((0.5 * t / numRevs) * sin(((t * 2) * π))), t, If[numRevs < 0, numRevs, 0], If[numRevs < 0, 0, numRevs]) → angleSpiral
  6. Segment((0, 0), P) → triSeg
  7. If(a > 0, (0.25, 0.2), (0.2, -0.2)) → LblThetaPos
  8. Segment(P, (0, y(P))) → triSeg_2
  9. Sequence(Segment[(-6.1, i), (-1.9, i)], i, -1, 1, 0.5) → horizontalGrid
  10. Sequence(Segment[(-6 + i, -1.1), (-6 + i, 1.1)], i, 0, 4, 0.25) → verticalGrid
  11. Segment((-6.1, 0), (-1.9, 0)) → horizontalAxis
  12. Segment((-4, -1.1), (-4, 1.1)) → verticalAxis
  13. Segment(P'', (x(P''), 0)) → Pseg
  14. LaTeX((((("\text{\textbf{Question: }" * MainInstruc) * "\\\textbf{Instructions: }") * SpecInstruc) * "}")) → allInstruc
  15. LaTeX((((("P'=(" * a) * "°,") * y(P'')) * ")")) → lblP'