MathPlotAI Logo MathPlotAI

Cotangent Law Demonstration

Cotangent Law Demonstration
Loading the math board and drawing, please wait…
2015-12-02 20:57
TriangleAngleTrigonometryGeometric Construction
This example dynamically demonstrates the application of the Cotangent Law in triangles, revealing the relationship between side lengths and cotangent values of angles. Key math concepts include trigonometric functions, cotangent law, and triangle geometry. Construction highlights from the GeoGebra command summary involve midpoint, semicircle, intersection, circle arc, polygon, orthogonal line, point, segment, ray, angle, and textfield. Suitable for high school and above learners to explore the integration of trigonometry and geometric constructions.

GeoGebra Commands & Parameters

  1. Midpoint(Q, P) → U_1
  2. Semicircle(Q, P) → s
  3. Intersect(Ray[P, Rotate[Q, α, P]], Ray[Q, Rotate[P, (-β), Q]]) → R
  4. Intersect(s, OrthogonalLine[Q, Line[R, Q]]) → A_1, B_1
  5. Intersect(s, OrthogonalLine[P, Line[R, P]]) → W, Z
  6. CircleArc(U_1, B_1, Z) → d_1
  7. Polygon(A, B, 3) → poly1, a, b, c, C
  8. Semicircle(B, A) → d
  9. Midpoint(A, B) → D
  10. OrthogonalLine(A, c) → e
  11. Intersect(d, e, 2) → E
  12. CircleArc(D, E, B) → f
  13. Point(f) → F
  14. Segment(A, F) → g
  15. OrthogonalLine(B, g) → h
  16. OrthogonalLine(C, h) → i
  17. OrthogonalLine(A, g) → j
  18. Intersect(i, j) → G
  19. Polygon(G, A, C) → poly2, c_1, g_1, a_1
  20. Intersect(h, i) → H
  21. Polygon(B, C, H) → poly3, h_1, b_1, c_2
  22. Polygon(B, A, F) → poly4, f_1, b_2, a_2
  23. Segment(I, J) → k
  24. Ray(J, Rotate[I, -90*°, J]) → l
  25. Ray(I, Rotate[J, 30*°, I]) → m
  26. Intersect(l, m) → L
  27. Point(Segment[J, L]) → K
  28. Polygon(I, K, 3) → poly5, n, p, q, M
  29. Intersect(l, Line[M, k]) → N
  30. Intersect(Line[M, k], Line[I, l]) → O
  31. Polygon(I, J, K) → poly6, k_1, i_1, j_1
  32. Polygon(K, M, N) → poly7, n_1, k_2, m_1
  33. Polygon(I, M, O) → poly8, o, i_2, m_2
  34. Polygon(P, Q, R) → poly9, r_1, p_1, q_1
  35. OrthogonalLine(P, q_1) → t
  36. Midpoint(P, Q) → T
  37. Angle(Q, P, R) → γ_1
  38. Angle(R, Q, P) → δ
  39. Textfield(α) → InputBox1
  40. Textfield(β) → InputBox2
  41. Angle(P, R, Q) → γ
  42. Point(d_1) → S
  43. Polygon(P, S, Q) → poly10, q_2, p_2, s_1
  44. Intersect(OrthogonalLine[R, p_2], Line[S, Q]) → V
  45. Intersect(OrthogonalLine[R, q_2], Line[S, P]) → U
  46. Polygon(R, V, Q) → poly11, q_3, r_2, v
  47. Polygon(R, U, P) → poly12, p_3, r_3, c_3