MathPlotAI Logo MathPlotAI

Construction of Trigonometric Function Graphs

Construction of Trigonometric Function Graphs
Loading the math board and drawing, please wait…
2015-06-05 15:18
FunctionTrigonometryGeometric ConstructionGraphing
This example demonstrates the construction of the graphs of the six trigonometric functions. Key math concepts include trigonometric functions, unit circle, and trigonometric identities. GeoGebra commands used in the construction are Circle, Point, Angle, Segment, OrthogonalLine, Line, Intersect, and Mirror. Suitable for high school students to learn and understand the geometric meaning of trigonometric function graphs.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → K
  3. Angle(B, A, K) → α
  4. Segment(A, K) → a
  5. Segment(B, C) → b
  6. OrthogonalLine(B, b) → d
  7. Line(A, K) → e
  8. Intersect(d, e) → L
  9. Segment(L, A) → f
  10. OrthogonalLine(K, xAxis) → g
  11. OrthogonalLine(A, xAxis) → h
  12. Line(K, xAxis) → i
  13. Intersect(h, i) → M
  14. Intersect(g, xAxis) → N
  15. Circle(A, N) → k
  16. Line(O, b) → j
  17. Line(B_1, C_1) → l
  18. Line(Z, A_1) → m
  19. Line(U, T) → n
  20. Intersect(c, h, 2) → D_1
  21. Intersect(c, h, 1) → E_1
  22. Intersect(c, xAxis, 1) → F_1
  23. Segment(K, N) → q
  24. Segment(B, L) → s
  25. Segment(K, N) → t
  26. Segment(A, N) → a_1
  27. Intersect(d, e) → G_1
  28. Circle(A, G_1) → c_1
  29. OrthogonalLine(D_1, h) → b_1
  30. Intersect(e, b_1) → H_1
  31. Circle(A, H_1) → d_1
  32. OrthogonalLine(E_1, h) → e_1
  33. Intersect(e, b_1) → I_1
  34. Segment(D_1, I_1) → h_1
  35. Mirror(D_1, g_1) → J_1
  36. Mirror(I_1, g_1) → K_1
  37. Segment(J_1, K_1) → i_1
  38. Segment(N_1, S) → f_1
  39. Segment(M_1, R) → k_1
  40. Segment(N_1, Q) → l_1
  41. Segment(M_1, P) → m_1
  42. Segment(N_1, U) → n_1
  43. Segment(M_1, T) → p_1
  44. Segment(A, G_1) → s_1
  45. Line(B, G_1) → p
  46. OrthogonalLine(K, xAxis) → q_1
  47. Intersect(q_1, xAxis) → V
  48. Segment(A, V) → r_1
  49. OrthogonalLine(W, h) → t_1
  50. Segment(N_1, P_1) → a_2
  51. Segment(O_1, M_1) → b_2
  52. Segment(V, K) → c_2
  53. OrthogonalLine(F_1, xAxis) → d_2
  54. Intersect(c_1, e, 2) → Q_1
  55. Segment(A, Q_1) → e_2
  56. Intersect(d_1, e, 2) → R_1
  57. Segment(A, H_1) → f_2
  58. Segment(A, R_1) → g_2
  59. OrthogonalLine(K, h) → h_2
  60. Intersect(h, h_2) → S_1
  61. Segment(K, S_1) → i_2
  62. Segment(A, I_1) → j_2

AI Drawing Prompt Reference

Draw a unit circle centered at the origin. Pick a point on the circle, connect it to the center to form a radius, and mark the angle between this radius and the horizontal diameter. From the point on the circle, drop a perpendicular to the horizontal diameter, and from the center, draw a perpendicular to the radius; these two perpendiculars intersect at a point, which is then connected to the center. Next, drop a perpendicular from the circle point to the horizontal axis, marking the foot, and draw a new circle centered at the origin with radius equal to the distance from the origin to that foot. Then construct a series of parallel and perpendicular lines to form a grid, using intersections and reflections to gradually outline the graphs of the six trigonometric functions, including sine, cosine, and tangent, with each curve defined by key intersection points and connecting segments.
The prompt above was compiled from the original drawing commands and is for reference only.