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Cobweb Diagram of Cosine Function

Cobweb Diagram of Cosine Function
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2014-02-23 19:28
FunctionTrigonometryCoordinate Geometry
This example demonstrates the cobweb diagram of the cosine function, showing the attracting property of the fixed point. Key mathematical concepts include functions, trigonometry, and geometric construction. Using GeoGebra commands such as Point and Segment, a series of points are constructed to visually illustrate the iterative process of the function. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a cobweb diagram for the cosine function to illustrate the attracting property of its fixed point. Start from a point on the x-axis, draw a vertical line segment upwards, then a horizontal line segment to the right, and repeat this process alternately to create a spiderweb pattern, visually demonstrating the iterative process of the function.
The prompt above was compiled from the original drawing commands and is for reference only.