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Unit Circle Sine Wave Trace Activity

Unit Circle Sine Wave Trace Activity
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2019-11-03 03:27
CircleTrigonometryCoordinate GeometryGraphing
This example demonstrates how to trace a sine wave by rotating a unit circle. It involves core math concepts like the unit circle, sine function, trigonometry, coordinate geometry, and continuity. GeoGebra commands used include Mirror, Segment, Circle, Point, OrthogonalLine, Intersect, Angle, CircleArc, Length, Sequence, Translate, Rotate, Line, and If. It is suitable for high school students learning about the generation of trigonometric function graphs and parametric equations.

GeoGebra Commands & Parameters

  1. Mirror(A_0, O) → E_0
  2. Segment(E_0, A_0) → b
  3. Circle(O, A_0) → circ
  4. Point(circ) → A
  5. OrthogonalLine(A, b) → a
  6. Segment(O, A) → hyp
  7. Intersect(a, b) → B
  8. Segment(B, A) → s
  9. Angle(A_0, O, A) → α
  10. Segment(O, B) → c
  11. Segment(C, CS_0) → cc
  12. CircleArc(O, A_0, A) → d
  13. Segment(C_1, C) → dd
  14. Length(d) → lend
  15. Point(d) → D
  16. Segment(S_1, S) → e
  17. Segment(CS_0, S) → f
  18. Angle(O, B, A) → β
  19. Sequence((((i * r) * π / 2), 0), i, 1, 4) → grad1
  20. Segment(B, A) → i
  21. Translate(Segment[O, Rotate[B, (p * π / 2), O]], Vector[(p * Vector[O, CS_0])]) → j
  22. Rotate(A_0, (α * hyp / Distance[A_0, H]), H) → A'
  23. CircleArc(H, A_0, A') → k
  24. Translate(Rotate[k, (p * π / 2), A'], Vector[(p * Vector[A', C_1])]) → q
  25. Translate(B, Vector[(p * Vector[A, S])]) → B'
  26. Translate(A, Vector[(p * Vector[A, S])]) → A'_1
  27. Segment(B', A'_1) → s'
  28. Translate(Rotate[k, (p * π / 2), A'], Vector[(p * Vector[A', S_1])]) → t_1
  29. OrthogonalLine(A_0, b) → l
  30. Line(O, A) → n
  31. Intersect(l, n) → T_1
  32. If(Defined[T_1], A_0, E_0) → E
  33. Segment(T, (x(T), 0)) → tt
  34. Segment(T, (0, y(T))) → a_1
  35. Translate(Rotate[k, (p * π / 2), A'], Vector[(p * Vector[A', (0, y(T))])]) → c_1
  36. Segment(A_0, T_1) → t
  37. Translate(A_0, Vector[(p * Vector[T_1, T])]) → F
  38. Translate(T_1, Vector[(p * Vector[T_1, T])]) → G
  39. Segment(F, G) → t'
  40. Angle(T_1, E, B) → γ
  41. Sequence(Text[" " + (i / 2) + " π r", (((i * r) * π / 2) - 0.2, (-0.5))], i, 1, 4) → grad2

AI Drawing Prompt Reference

Draw a unit circle and rotate a point A on it. Draw a line a that is orthogonal to OA, intersecting the circle at point B. Draw a line segment OB and then draw another line segment s through B. Calculate angle α, and then use rotation and translation to generate a series of points and line segments, forming a sine wave trace.
The prompt above was compiled from the original drawing commands and is for reference only.