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正弦与余弦函数建模

正弦与余弦函数建模
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2015-09-29 09:49
函数三角函数参数方程
本范例通过正弦和余弦函数建模，演示了周期性现象。核心数学概念包括三角函数、函数图像和参数方程。使用了Intersect、Point、OrthogonalLine等GeoGebra命令。适合高中数学教学和学习。

GeoGebra 命令及参数

  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