Basic Trigonometric Ratio Problem Exercises Generator

Basic Trigonometric Ratio Problem Exercises Generator
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2013-07-16 05:55
This applet generates diagrams for basic trigonometric ratio problem exercises. It involves concepts of sine, cosine, and ratios. Using GeoGebra commands such as Intersect, Point, Segment, OrthogonalLine, Circle, Angle, Rotate, etc., various geometric shapes can be constructed. Suitable for middle and high school students to learn and practice trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(Circle[A, l_1]) → B
  3. Segment(A, B) → a
  4. OrthogonalLine(A, a) → b
  5. Circle(A, l_2) → c
  6. Intersect(c, b) → C_1, C
  7. Segment(A, C) → d
  8. Segment(B, C) → e
  9. Angle(B, A, C) → α
  10. Point(xAxis) → D
  11. Point(Circle[D, l_1]) → E
  12. Segment(D, E) → f
  13. OrthogonalLine(D, f) → g
  14. Rotate(D, -θ_1, E) → D'
  15. Angle(D', E, D) → θ
  16. Line(E, D') → h
  17. Intersect(h, g) → F
  18. Segment(E, F) → i
  19. Segment(D, F) → j
  20. Angle(E, D, F) → β
  21. Distance(f, j) → k
  22. Distance(e, a) → l
  23. Angle(C, B, A) → γ
  24. Point(Circle[G, l_1]) → H
  25. Segment(G, H) → m
  26. OrthogonalLine(G, m) → n
  27. Circle(H, l_2) → p
  28. Intersect(p, n) → I, J
  29. Segment(H, J) → q
  30. Segment(G, J) → r
  31. Angle(H, G, J) → δ
  32. Angle(J, H, G) → ε
  33. Point(Circle[K, l_1]) → L
  34. Segment(K, L) → s
  35. Circle(L, l_2) → t
  36. OrthogonalLine(K, s) → a_1
  37. Intersect(t, a_1) → M, N
  38. Segment(L, M) → b_1
  39. Segment(K, M) → c_1
  40. Angle(M, K, L) → ζ
  41. Angle(L, M, K) → η
  42. Point(Circle[P, l_2]) → Q
  43. Segment(P, Q) → d_1
  44. Rotate(Q, θ_1, P) → Q'
  45. Angle(Q, P, Q') → ι
  46. Rotate(P, -(90° - θ_1), Q) → P'
  47. Angle(P', Q, P) → κ
  48. Line(P, Q') → e_1
  49. Line(Q, P') → f_1
  50. Intersect(e_1, f_1) → R
  51. Segment(Q, R) → g_1
  52. Segment(P, R) → h_1
  53. Angle(P, R, Q) → λ
  54. Point(Circle[S, l_2]) → T
  55. Segment(S, T) → i_1
  56. OrthogonalLine(T, i_1) → j_1
  57. Rotate(T, 90° - θ_1, S) → T'
  58. Angle(T, S, T') → μ
  59. Line(S, T') → k_1
  60. Intersect(j_1, k_1) → U
  61. Segment(T, U) → m_1
  62. Segment(S, U) → n_1
  63. Angle(U, T, S) → ν
  64. Angle(S, U, T) → ξ
  65. Point(Circle[V, l_1]) → W
  66. Segment(V, W) → s_1
  67. Circle(W, l_2) → t_1
  68. OrthogonalLine(V, s_1) → a_2
  69. Intersect(t_1, a_2) → X, N_1
  70. Segment(W, X) → b_2
  71. Segment(V, X) → c_2
  72. Angle(X, V, W) → ζ_1
  73. Angle(X, W, V) → η_1

AI Drawing Prompt Reference

Draw a right triangle ABC with AB as the base, AC as the hypotenuse, and ∠BAC as the right angle. Then take a point D on AB and draw a circle with D as the center, intersecting AC at point E, with DE as the chord. Construct the perpendicular line to DE intersecting AC at point F, and connect DF. Next, rotate DE counterclockwise by θ1 degrees around D to get DE', and construct ∠ED'E. Then draw a circle with E as the center, intersecting DE' at point F', and connect EF'. Construct the perpendicular line to EF' intersecting DE at point G, and connect EG. Finally, rotate EF' counterclockwise by (90°-θ1) degrees around E to get EF'', and construct ∠FE'F''.
The prompt above was compiled from the original drawing commands and is for reference only.