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Modeling with Sine and Cosine Functions

Modeling with Sine and Cosine Functions
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2015-09-29 09:49
FunctionTrigonometryParametric Equation
This example demonstrates periodic phenomena using sine and cosine functions. Key mathematical concepts include trigonometric functions, function graphs, and parametric equations. GeoGebra commands used include Intersect, Point, OrthogonalLine, etc. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → Origin
  2. Point(Unit) → C
  3. OrthogonalLine(C, xAxis) → a
  4. Intersect(xAxis, a) → PtCosOnX
  5. Segment(C, PtCosOnX) → sine
  6. Segment(Origin, C) → r
  7. CircleSector(Origin, Pt1, C) → sectortheta
  8. OrthogonalLine(C, r) → b
  9. CircleArc(Origin, Pt1, C) → arctheta
  10. OrthogonalLine(C, yAxis) → c
  11. Rotate(Pt1, 0.5235987755982988, Origin) → Piovr6
  12. Rotate(Pt1, 0.7853981633974483, Origin) → Piovr4
  13. Rotate(Pt1, 1.0471975511965976, Origin) → Piovr3
  14. Intersect(Unit, yAxis) → Pi3ovr2, Piovr2
  15. Rotate(Piovr2, 0.5235987755982988, Origin) → Pi2ovr3
  16. Rotate(Piovr2, 0.7853981633974483, Origin) → Pi3ovr4
  17. Rotate(Piovr2, 1.0471975511965976, Origin) → Pi5ovr6
  18. Intersect(Unit, xAxis) → Pi1, Pi02Pi
  19. Mirror(Pi2ovr3, xAxis) → Pi4ovr3
  20. Mirror(Pi3ovr4, xAxis) → Pi5ovr4
  21. Mirror(Pi5ovr6, xAxis) → Pi7ovr6
  22. Mirror(Piovr6, xAxis) → Pi11ovr6
  23. Mirror(Piovr4, xAxis) → Pi7ovr4
  24. Mirror(Piovr3, xAxis) → Pi5ovr3
  25. OrthogonalLine(C, yAxis) → d
  26. Intersect(yAxis, d) → PtSinOnY
  27. Segment(PtSinOnY, C) → e
  28. Angle(Pi02Pi, Origin, C) → angletheta
  29. Rotate(Piovr2, -angletheta, Origin) → Piovr2'
  30. Angle(Piovr2', Origin, Piovr2) → angleNegtheta
  31. Segment(Origin, Piovr2') → g
  32. Angle(Pi02Pi, Origin, Piovr2') → anglePiovr2mintheta
  33. OrthogonalLine(Piovr2', yAxis) → f
  34. OrthogonalLine(Piovr2', xAxis) → i
  35. Intersect(f, yAxis) → A
  36. Intersect(i, xAxis) → B
  37. Segment(A, Piovr2') → j
  38. Segment(B, Piovr2') → k
  39. Angle(Piovr2', Origin, Pi02Pi) → anglePiovr2neg