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Unit Circle Investigation 1

Unit Circle Investigation 1
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2017-09-20 09:30
CircleVectorTrigonometryMatrixGeometric Construction
This example demonstrates the relationship between the unit circle and trigonometric functions through dynamic interaction, showing the correspondence between angles and coordinates. Core mathematical concepts include the unit circle, trigonometric functions, vectors, and matrix transformations. GeoGebra commands used in construction are Intersect, Circle, Point, Segment, Rotate, Angle, and OrthogonalLine. Suitable for high school mathematics teaching to understand the definition of trigonometric functions and vector matrix representation.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → B
  4. Intersect(c, xAxis, 1) → π1
  5. Intersect(c, xAxis, 2) → zero
  6. Segment(π1, zero) → a
  7. Intersect(c, yAxis, 2) → π2
  8. Intersect(c, yAxis, 1) → π3_2
  9. Segment(π2, π3_2) → b
  10. Point(c) → π6
  11. Rotate(zero, θ, A) → D'
  12. Angle(zero, A, D') → α
  13. Segment(A, D') → i
  14. OrthogonalLine(D', a) → j
  15. OrthogonalLine(D', b) → k
  16. Intersect(j, a) → Q
  17. Segment(A, Q) → l
  18. Segment(D', Q) → m
  19. Intersect(c, i, 1) → point
  20. Point(c) → π3
  21. Point(c) → π4
  22. Point(c) → π2_3
  23. Point(c) → π3_4
  24. Point(c) → π5_6
  25. Point(c) → π7_6
  26. Point(c) → π5_4
  27. Point(c) → π4_3
  28. Point(c) → π5_3
  29. Point(c) → π7_4
  30. Point(c) → π11_6
  31. Segment(π2_3, π3) → n
  32. Segment(π3_4, π4) → p
  33. Segment(π5_6, π6) → q
  34. Segment(π7_6, π11_6) → r
  35. Segment(π5_4, π7_4) → s
  36. Segment(π4_3, π5_3) → t
  37. Segment(π6, π11_6) → a_1
  38. Segment(π4, π7_4) → b_1
  39. Segment(π3, π5_3) → c_1
  40. Segment(π2_3, π4_3) → d
  41. Segment(π3_4, π5_4) → e
  42. Segment(π5_6, π7_6) → f

AI Drawing Prompt Reference

Draw a unit circle and dynamically plot an angle θ, find the corresponding sine and cosine values by rotation and intersection, use vertical lines to represent sine values, and horizontal lines to represent cosine values, illustrating the relationship between the unit circle and trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.