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Dynamic Demonstration of Trigonometric Circle

Dynamic Demonstration of Trigonometric Circle
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2017-02-23 01:48
CircleVectorFunctionTrigonometryGeometric Construction
This example demonstrates the dynamic changes of trigonometric circles, involving core mathematical concepts such as trigonometric functions, circles, and vectors. Using GeoGebra commands like Point, Intersect, Circle, Segment, etc., it dynamically shows the graphs of A*sin(Bx+C) and A*cos(Bx+C). Suitable for high school mathematics teaching, especially in coordinate geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Point(q) → N
  2. Intersect(xAxis, yAxis) → A_1
  3. Circle(A_1, B_1) → c
  4. Segment(A_1, C_2) → a
  5. Segment(B_1, A_1) → b
  6. Angle(B_1, A_1, C_2) → α
  7. OrthogonalLine(C_2, yAxis) → d
  8. Intersect(d, yAxis) → D
  9. CircleArc(A_1, B_1, C_2) → e
  10. Vector(C_2, D) → u
  11. Vector(E, F) → v
  12. Segment(D, A_1) → h
  13. Segment(H, B_1) → i
  14. Vector(t, C_2) → w
  15. OrthogonalLine(C_2, b) → j
  16. Intersect(j, i) → I
  17. Vector(C_2, I) → z
  18. Vector(I, J) → k
  19. Vector(E, K) → l
  20. Vector(L, K) → n
  21. Vector(M, C_2) → p
  22. Vector(N, t) → r
  23. Vector(N, E) → s
  24. Sequence(w, w, -6.283185307179586, 6.283185307179586, 0.5235987755982988) → pis
  25. Zip((-2.5, p), p, pis) → list1
  26. Zip((-1.5, p), p, pis) → list2
  27. Vector(O, M) → u_1
  28. Vector(O, L) → v_1
  29. Vector(L, F) → w_1
  30. Segment(O, N) → a_1
  31. Segment(E, L) → b_1
  32. Segment(M, t) → c_1
  33. Dilate(e, A, A_1) → e'
  34. Dilate(c, A, A_1) → c'
  35. Dilate(C_2, A, A_1) → C'
  36. Dilate(I, A, A_1) → I'
  37. Dilate(D, A, A_1) → D'
  38. Vector(C', D') → m
  39. Vector(C', I') → d_1
  40. Segment(C', C_2) → f_1
  41. Vector(F, Q) → e_1
  42. Vector(K, P) → h_1
  43. Dilate(H, A, A_1) → H'
  44. Dilate(B_1, A, A_1) → R
  45. Segment(H', R) → i'
  46. Dilate(J, A, A_1) → J'
  47. Vector(I', J') → i_1
  48. CircleArc(A_1, C_2, B_1) → k_1
  49. Dilate(k_1, A, A_1) → p_1

AI Drawing Prompt Reference

Draw a dynamic trigonometric circle showing sine and cosine functions, involving a circle, axes, points, and vectors. Construct using orthogonal lines and angles, demonstrating the relationship between trigonometric functions and the circle, suitable for high school math teaching.
The prompt above was compiled from the original drawing commands and is for reference only.