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Unit Circle Transformations

Unit Circle Transformations
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2020-12-18 04:48
CircleTrigonometryTransformation
This example demonstrates transformations of trigonometric functions on the unit circle. Key mathematical concepts include trigonometric functions and the unit circle. Using GeoGebra commands such as Rotate, Angle, and Segment, dynamic displays of translations, stretches, and rotations of trigonometric functions are shown. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Textfield(p) → InputBox1
  2. Textfield(b) → InputBox2
  3. Textfield(s) → InputBox3
  4. Rotate(A', 30°, A) → A''
  5. Angle(A', A, A'') → α
  6. Segment(A, A'') → g
  7. Rotate(A', 45°, A) → A''_{1}
  8. Angle(A', A, A''_{1}) → β
  9. Segment(A, A''_{1}) → h
  10. Rotate(A', 60°, A) → A''_{2}
  11. Angle(A', A, A''_{2}) → γ
  12. Segment(A, A''_{2}) → i
  13. Point(f) → D
  14. Rotate(A', 120°, A) → A''_{3}
  15. Angle(A', A, A''_{3}) → δ
  16. Segment(A, A''_{3}) → l
  17. Rotate(A', 135°, A) → A''_{4}
  18. Angle(A', A, A''_{4}) → ε
  19. Segment(A, A''_{4}) → m
  20. Rotate(A', 150°, A) → A''_{5}
  21. Angle(A', A, A''_{5}) → ζ
  22. Segment(A, A''_{5}) → n
  23. Rotate(A', 180°, A) → A''_{6}
  24. Angle(A', A, A''_{6}) → η
  25. Segment(A, A''_{6}) → q
  26. Rotate(A', 90°, A) → A''_{7}
  27. Angle(A', A, A''_{7}) → θ
  28. Segment(A, A''_{7}) → j
  29. Rotate(A', 0°, A) → A''_{8}
  30. Angle(A', A, A''_{8}) → ι
  31. Segment(A, A') → k
  32. Rotate(A', 210°, A) → A''_{9}
  33. Angle(A', A, A''_{9}) → κ
  34. Segment(A, A''_{9}) → r
  35. Rotate(A', 225°, A) → A''_{10}
  36. Angle(A', A, A''_{10}) → λ
  37. Segment(A, A''_{10}) → t
  38. Rotate(A', 240°, A) → A''_{11}
  39. Angle(A', A, A''_{11}) → μ
  40. Segment(A, A''_{11}) → a
  41. Rotate(A', 270°, A) → A''_{12}
  42. Angle(A', A, A''_{12}) → ν
  43. Segment(A, A''_{12}) → c
  44. Rotate(A', 300°, A) → A''_{13}
  45. Angle(A', A, A''_{13}) → ξ
  46. Segment(A, A''_{13}) → d
  47. Rotate(A', 315°, A) → A''_{14}
  48. Angle(A', A, A''_{14}) → ο
  49. Segment(A, A''_{14}) → e
  50. Rotate(A', 330°, A) → A''_{15}
  51. Angle(A', A, A''_{15}) → ρ
  52. Segment(A, A''_{15}) → f_1
  53. Intersect(f, j, 1) → B
  54. Point(f) → C
  55. Intersect(f, q, 1) → E
  56. Intersect(f, c, 1) → F

AI Drawing Prompt Reference

Draw a unit circle with center A and a point A' on the circle. From A, draw segments to A' and to points obtained by rotating A' around A by specific angles: 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, and 315°. Label the angle between each segment and the initial radius. Place a movable point D on the circle. Include three input boxes for parameters p, b, and s to dynamically adjust transformations. The figure illustrates angle and segment relationships on the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.