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F.4 Trigonometric Function (Sine) Dynamic Demo

F.4 Trigonometric Function (Sine) Dynamic Demo
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2017-05-15 15:10
CircleAngleFunctionTrigonometrySlider Animation
① This example dynamically illustrates the geometric definition of the sine function using a unit circle, showing how the angle maps to a point on the sine curve and how the graph is generated. ② Core mathematical concepts include the sine function, unit circle, angle and radian measure, periodicity, and the relationship between geometric constructions and function graphs. ③ Construction highlights: uses GeoGebra commands such as Segment, Circle, Intersect, Rotate, OrthogonalLine, Point, Ray, Angle, Textfield, Midpoint, Vector, If, and Polygon, with objects like a slider (Play_1) for animation and multiple text fields for dynamic labels. ④ Suitable for senior secondary students (e.g., DSE F.4 or equivalent) learning trigonometry, useful for classroom demonstrations, interactive exploration, and understanding the sine function's geometric origin and graphical representation.

GeoGebra Commands & Parameters

  1. Segment(O, B_1) → h_1
  2. Circle(O, 3.141592653589793) → c
  3. Intersect(c, h_1) → D_1,
  4. Rotate(D_1, x(W), O) → A_2
  5. Intersect(xAxis, yAxis) → Origin
  6. Segment(Origin, O) → h
  7. Intersect(c, h) → D,
  8. OrthogonalLine(D, xAxis) → c_1
  9. Rotate(D, x(W), O) → A
  10. OrthogonalLine(A, xAxis) → g
  11. Intersect(g, xAxis) → B
  12. Segment(B, O) → k
  13. Segment(O, A) → b
  14. Intersect(b, k) → E
  15. Segment(A_2, O) → b_1
  16. Intersect(b_1, c_1) → F
  17. OrthogonalLine(Origin, xAxis) → d
  18. OrthogonalLine(Origin, d) → f
  19. Point(xAxis) → G
  20. Ray(Origin, G) → m
  21. Angle(D, O, A) → β
  22. Textfield(Θ) → inputBox1
  23. Segment(O, D) → a
  24. OrthogonalLine(A, a) → e
  25. Segment(A, B) → j
  26. Segment(A, X) → l
  27. Segment(W, Origin) → n
  28. Segment(X, W) → q
  29. Segment(W, Y) → s
  30. Segment(W, Z) → t
  31. Angle(A, B, O) → γ
  32. Segment(F, D) → d_1
  33. Segment(F, A) → e_1
  34. Midpoint(q) → H
  35. Midpoint(s) → I
  36. Midpoint(t) → S
  37. Segment(B, O) → p
  38. Point(yAxis) → P
  39. Point(yAxis) → Q
  40. Vector(P, Q) → u
  41. Point(u) → R
  42. Point(xAxis) → T
  43. Textfield(speed) → inputBox2
  44. Angle(T, W, X) → δ
  45. Angle(T, W, Y) → ε
  46. Vector(U, V) → z
  47. Vector(A_1, B_1) → u_1
  48. Vector(A_1, B_1) → v_1
  49. Vector(C_1, T) → v
  50. Vector(V, U) → z_1
  51. Segment(A_2, Y) → I_1
  52. Angle(D_1, O, A_2) → β_1
  53. OrthogonalLine(A_2, xAxis) → g_1
  54. Intersect(g_1, xAxis) → B_2
  55. Segment(A_2, B_2) → a_1
  56. Angle(A_2, B_2, O) → γ_1
  57. If(f_1 ≟ 1, true, false) → FA
  58. If(f_1 ≟ 0, true, false) → FB
  59. Polygon(E_1, F_1, G_1, H_1) → poly1, e_2, f_2, g_2, h_2

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with radius approximately π. From the center, draw a horizontal ray as the initial side. Place a point on the circle and rotate it by a dynamic angle, showing the angle in radians. Drop a perpendicular from the circle point to the horizontal axis, marking the foot. Connect the center to the circle point to form a radius. Outside the circle, set up coordinate axes and map the y-coordinate of the circle point to the horizontal axis to generate the corresponding point on the sine curve. Add a slider to control the angle and display dynamic text for the angle and sine value. Connect relevant points with segments to form a right triangle, labeling the angle and side relationships.
The prompt above was compiled from the original drawing commands and is for reference only.