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New Trig IDs from Similar Right Triangles (V2)

New Trig IDs from Similar Right Triangles (V2)
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2018-10-28 00:37
TriangleFunctionTrigonometryTransformationGeometric Construction
In collections Trigonometric Identities
This example demonstrates how to derive new trigonometric identities using similar right triangles. Key math concepts include similarity transformations, secant lines, and trigonometric functions. GeoGebra commands and objects used in the construction are Circle, Tangent, Segment, Intersect, OrthogonalLine, Line, Point, Angle, Rotate, CircleSector, Dilate, Vector, and Translate. Suitable for high school mathematics education to understand and apply trigonometric identities.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Tangent(A, c) → a,
  3. Segment(O, A) → e
  4. Intersect(a, b) → B
  5. Intersect(a, d) → C
  6. OrthogonalLine(A, b) → f
  7. OrthogonalLine(A, d) → g
  8. Intersect(d, g) → D
  9. Intersect(b, f) → E
  10. Segment(A, B) → h
  11. Segment(O, E) → i
  12. Segment(E, A) → j
  13. Segment(A, C) → k
  14. Line(O, A) → l
  15. Line(D, A) → m
  16. Line(C, m) → n
  17. Point(n) → F
  18. OrthogonalLine(F, n) → p
  19. Intersect(b, p) → G
  20. Segment(G, F) → q
  21. OrthogonalLine(B, m) → r
  22. Point(d) → H
  23. OrthogonalLine(H, d) → s
  24. Intersect(r, s) → I
  25. Segment(H, I) → t
  26. Angle(A, E, O) → α
  27. Intersect(l, n) → J
  28. Angle(G, F, C) → γ
  29. Intersect(c, yAxis, 2) → K
  30. Segment(O, K) → a_1
  31. Angle(t, yAxis) → δ
  32. Angle(xAxis, q) → ε
  33. Angle(B, I, H) → ζ
  34. Angle(E, O, A) → η
  35. Angle(E, A, B) → ι
  36. Point(c) → L
  37. Segment(O, L) → f_1
  38. Intersect(n, r) → M
  39. Intersect(xAxis, r) → N
  40. Intersect(n, a) → P
  41. Angle(P, M, N) → κ
  42. Circle(O, (0.4 * i)) → c_1
  43. Intersect(c_1, xAxis) → Q, R
  44. Rotate(R, If[0 < u ≤ 1, ((o * π / 180) * u), (o * π / 180)], O) → R'
  45. CircleSector(O, R, R') → d_1
  46. Dilate(O, If[1.5 < u ≤ 2.5, 2.5 - u, 0], A) → O'
  47. Vector(O, O') → v
  48. Translate(d_1, v) → e_1
  49. Rotate(e_1, If[2.5 < u ≤ 3.5, ((-(u - 2.5)) * π / 2), ((-π)) / 2], A) → g_1
  50. Dilate(A, If[3.5 < u ≤ 4.5, 4.5 - u, 0], P) → A'
  51. Vector(A, A') → w
  52. Translate(g_1, w) → h_1
  53. Segment(F, M) → i_1
  54. Segment(N, M) → j_1
  55. Segment(N, I) → k_1
  56. Intersect(xAxis, q) → S

AI Drawing Prompt Reference

To describe a graph based on similar right triangles, including circles, tangents, line segments, intersection points, perpendicular lines, straight lines, points, angles, rotation, sectors, scaling, and translation. Describe the construction order of these objects.
The prompt above was compiled from the original drawing commands and is for reference only.