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Cosine Function Demonstration

Cosine Function Demonstration
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2017-06-01 16:20
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example illustrates the geometric interpretation of the cosine function by dynamically rotating to show the relationship between angles and cosine values. Key mathematical concepts include trigonometry, vectors, coordinate geometry, and geometric transformations. Construction highlights the use of GeoGebra commands such as Segment, Circle, Intersect, Rotate, OrthogonalLine, Point, Ray, Angle, Textfield, Midpoint, Vector, If, and Polygon. Suitable for high school mathematics education, helping students understand the generation of trigonometric function graphs and the application of parametric equations.

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 a dynamic illustration showing the geometric meaning of the cosine function, featuring a rotating circle and coordinate axes, with intersection points and line relationships demonstrating the correspondence between angles and cosine values, and label key angles and vectors to illustrate the generation process of trigonometric function graphs and parametric equations.
The prompt above was compiled from the original drawing commands and is for reference only.