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余弦函数的蛛网图

余弦函数的蛛网图
几何画板及绘图内容加载中，请稍等……
2014-02-23 19:28
函数三角函数解析几何
该范例演示了余弦函数的蛛网图，展示了固定点对任意点的吸引特性。核心数学概念包括函数、三角函数和几何作图。通过使用GeoGebra命令如Point、Segment等，可以构造出一系列点，直观地展示函数的迭代过程。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Segment((A1, A2), (A2, A2)) → C1
  3. Segment((A2, A2), (A2, A3)) → B2
  4. Segment((A2, A3), (A3, A3)) → C2
  5. Segment((A3, A3), (A3, A4)) → B3
  6. Segment((A3, A4), (A4, A4)) → C3
  7. Segment((A4, A4), (A4, A5)) → B4
  8. Segment((A4, A5), (A5, A5)) → C4
  9. Segment((A5, A5), (A5, A6)) → B5
  10. Segment((A5, A6), (A6, A6)) → C5
  11. Segment((A6, A6), (A6, A7)) → B6
  12. Segment((A6, A7), (A7, A7)) → C6
  13. Segment((A7, A7), (A7, A8)) → B7
  14. Segment((A7, A8), (A8, A8)) → C7
  15. Segment((A8, A8), (A8, A9)) → B8
  16. Segment((A8, A9), (A9, A9)) → C8
  17. Segment((A9, A9), (A9, A10)) → B9
  18. Segment((A9, A10), (A10, A10)) → C9
  19. Segment((A10, A10), (A10, A11)) → B10
  20. Segment((A10, A11), (A11, A11)) → C10
  21. Segment((A11, A11), (A11, A12)) → B11
  22. Segment((A11, A12), (A12, A12)) → C11
  23. Segment((A12, A12), (A12, A13)) → B12
  24. Segment((A12, A13), (A13, A13)) → C12
  25. Segment((A13, A13), (A13, A14)) → B13
  26. Segment((A13, A14), (A14, A14)) → C13
  27. Segment((A14, A14), (A14, A15)) → B14
  28. Segment((A14, A15), (A15, A15)) → C14
  29. Segment((A15, A15), (A15, A16)) → B15
  30. Segment((A15, A16), (A16, A16)) → C15
  31. Segment((A16, A16), (A16, A17)) → B16
  32. Segment((A16, A17), (A17, A17)) → C16
  33. Segment((A17, A17), (A17, A18)) → B17
  34. Segment((A17, A18), (A18, A18)) → C17
  35. Segment((A1, 0), (A1, A2)) → b

AI 绘图提示语参考

画一个余弦函数的蛛网图，展示固定点的吸引特性。从x轴上的一点开始，先垂直向上画一条线段，再水平向右画一条线段，然后重复此过程，交替绘制垂直和水平线段，形成蛛网状图案，直观展示函数的迭代过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。