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Ferris Wheel Height vs. Time Function

Ferris Wheel Height vs. Time Function
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2017-06-14 07:55
FunctionTrigonometryCalculusGeometric Construction
This example demonstrates the sine function graph of a Ferris wheel's height over time during operation. Core math concepts include sine functions, differential calculus, linear equations, and geometric transformations. Construction highlights involve GeoGebra commands like Circle, Segment, Rotate, Angle, Line, OrthogonalLine, Intersect, and Distance. Suitable for high school students learning function graphs, trigonometric applications, and geometric transformations, ideal for classroom instruction or self-study.

GeoGebra Commands & Parameters

  1. Circle(C, 50) → c
  2. Segment(C, G1) → a
  3. Segment(C, G2) → b
  4. Rotate(Zero, α, C) → Zero'
  5. Angle(Zero, C, Zero') → β
  6. Segment(C, Zero') → d
  7. Rotate(Zero, 30° + α, C) → Zero'_1
  8. Angle(Zero, C, Zero'_1) → γ
  9. Segment(C, Zero'_1) → e
  10. Rotate(Zero, 60° + α, C) → Zero'_2
  11. Angle(Zero, C, Zero'_2) → δ
  12. Segment(C, Zero'_2) → f
  13. Rotate(Zero, 90° + α, C) → Zero'_3
  14. Angle(Zero, C, Zero'_3) → ε
  15. Segment(Zero'_3, C) → g
  16. Rotate(Zero, 120° + α, C) → Zero'_4
  17. Angle(Zero, C, Zero'_4) → ζ
  18. Segment(Zero'_4, C) → h
  19. Rotate(Zero, 150° + α, C) → Zero'_5
  20. Angle(Zero, C, Zero'_5) → η
  21. Segment(Zero'_5, C) → i
  22. Rotate(Zero, 180° + α, C) → Zero'_6
  23. Angle(Zero, C, Zero'_6) → θ
  24. Segment(Zero'_6, C) → j
  25. Rotate(Zero, 210° + α, C) → Zero'_7
  26. Angle(Zero, C, Zero'_7) → ι
  27. Segment(Zero'_7, C) → k
  28. Rotate(Zero, 240° + α, C) → Zero'_8
  29. Angle(Zero, C, Zero'_8) → κ
  30. Segment(Zero'_8, C) → l
  31. Rotate(Zero, 270° + α, C) → Zero'_9
  32. Angle(Zero, C, Zero'_9) → λ
  33. Segment(Zero'_9, C) → m
  34. Rotate(Zero, 300° + α, C) → Zero'_{10}
  35. Angle(Zero, C, Zero'_{10}) → μ
  36. Segment(Zero'_{10}, C) → n
  37. Rotate(Zero, 330° + α, C) → Zero'_{11}
  38. Angle(Zero, C, Zero'_{11}) → ν
  39. Segment(Zero'_{11}, C) → p
  40. Line(G1, G2) → q
  41. OrthogonalLine(Zero', q) → r
  42. Intersect(r, q) → A
  43. Segment(Zero', A) → s
  44. OrthogonalLine(Zero'_1, d) → t
  45. Intersect(d, t) → B
  46. OrthogonalLine(Zero'_2, d) → b_1
  47. Intersect(b_1, d) → D
  48. Distance(D, C) → distanceDC

AI Drawing Prompt Reference

Draw a Ferris wheel with a fixed center and radius 50. From the center, draw 12 radial segments to equally spaced points on the circle, each 30 degrees apart, and label the angle between each radius and the initial horizontal radius. The wheel can rotate by a variable angle. Below the wheel, draw a horizontal line as the ground. From each marked point on the circle, drop a perpendicular to the ground, marking the foot. Specifically, from the point on the initial radius, drop a perpendicular to the ground and measure its length to show the height variation over time.
The prompt above was compiled from the original drawing commands and is for reference only.