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Sine Function Geometric Representation

Sine Function Geometric Representation
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2017-06-01 16:06
FunctionTrigonometryGraphing
This example demonstrates the geometric representation of the sine function. It involves the core mathematical concept of trigonometry. Using GeoGebra commands such as Segment, Circle, Intersect, etc., the sine function's graph can be constructed. Suitable for high school mathematics education, helping students understand the properties and graph characteristics of the sine function.

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(W, Origin) → n
  27. Segment(X, W) → q
  28. Segment(W, Y) → s
  29. Segment(W, Z) → t
  30. Angle(A, B, O) → γ
  31. Segment(F, D) → d_1
  32. Segment(F, A) → e_1
  33. Midpoint(q) → H
  34. Midpoint(s) → I
  35. Midpoint(t) → S
  36. Segment(B, O) → p
  37. Point(yAxis) → P
  38. Point(yAxis) → Q
  39. Vector(P, Q) → u
  40. Point(u) → R
  41. Point(xAxis) → T
  42. Textfield(speed) → inputBox2
  43. Angle(T, W, X) → δ
  44. Angle(T, W, Y) → ε
  45. Vector(U, V) → z
  46. Vector(A_1, B_1) → u_1
  47. Vector(A_1, B_1) → v_1
  48. Vector(C_1, T) → v
  49. Vector(V, U) → z_1
  50. Segment(A_2, Y) → I_1
  51. Angle(D_1, O, A_2) → β_1
  52. OrthogonalLine(A_2, xAxis) → g_1
  53. Intersect(g_1, xAxis) → B_2
  54. Segment(A_2, B_2) → a_1
  55. Angle(A_2, B_2, O) → γ_1
  56. If(f_1 ≟ 1, true, false) → FA
  57. If(f_1 ≟ 0, true, false) → FB
  58. Polygon(E_1, F_1, G_1, H_1) → poly1, e_2, f_2, g_2, h_2

AI Drawing Prompt Reference

Draw the geometric representation of the sine function. Start by drawing the unit circle and the x-axis, then use rotation and intersection to find the points corresponding to the sine values, and finally draw the graph of the sine function. Specifically, draw the unit circle, x-axis, and origin, use rotation and intersection to find the points corresponding to the sine values, and then draw the sine function's graph.
The prompt above was compiled from the original drawing commands and is for reference only.