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Trigonometric Circle Intersection Demo

Trigonometric Circle Intersection Demo
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2017-02-04 01:14
CircleTrigonometryCoordinate GeometryGeometric ConstructionSlider Animation
In collections Mapping Diagrams: From AB to C&DE, Resource
This example dynamically demonstrates the intersection points between trigonometric functions and a circle, visually integrating geometry with algebra. Core math concepts include trigonometric functions, circle equations, analytical geometry, and conditional probability. Construction highlights from the summary involve commands like Intersect, Circle, Segment, Angle, OrthogonalLine, CircleArc, Vector, Sequence, Line, and Point in GeoGebra. Suitable for high school and above learners to understand trigonometric graphs, geometric properties, and computational methods.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Segment(A, C) → a
  4. Segment(B, A) → b
  5. Angle(B, A, C) → α
  6. OrthogonalLine(C, yAxis) → d
  7. Intersect(d, yAxis) → D
  8. CircleArc(A, B, C) → e
  9. Vector(C, D) → u
  10. Vector(E, F) → v
  11. Segment(D, A) → h
  12. Segment(H, B) → i
  13. Vector(t, C) → w
  14. Sequence((-1.5, t), t, -87.96459430051421, 87.96459430051421, 0.2617993877991494) → tval
  15. Vector(E, J) → z
  16. Vector(C, K) → j
  17. Vector(A, L) → k
  18. Segment(B, L) → l
  19. Vector(E, M) → m
  20. Line(L, B) → n
  21. CircleArc(A, C, B) → p
  22. Angle(C, A, B) → β
  23. Segment(A, K) → q
  24. Vector(A, O) → u_1
  25. Vector(A, O) → m_1
  26. Point(s) → P
  27. Segment(P, O) → a_1
  28. Vector(E, Q) → v_1
  29. Vector(J, T) → w_1
  30. Vector(F, S) → z_1
  31. Vector(M, R) → d_1
  32. Vector(E, R) → f_1
  33. Vector(E, T) → g_1
  34. Vector(E, S) → h_1
  35. CircleArc(A, L, Z) → p_1
  36. Vector(L, Z) → l_1
  37. Vector(A, L) → k_1
  38. CircleArc(A, O, A_1) → q_1
  39. Vector(A, A_1) → b_1
  40. Line(A, C) → j_1
  41. CircleArc(A, L, B_1) → r_1
  42. Vector(A, B_1) → n_1