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New Trig IDs From Similar Right Triangles

New Trig IDs From Similar Right Triangles
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2018-10-26 00:39
TriangleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to derive new trigonometric identities using similar right triangles. Key math concepts include similarity, trigonometric definitions, and angle relationships. GeoGebra commands/objects used are Intersect, Circle, Rotate, Ray, OrthogonalLine, Line, Angle, Segment, and Point. Suitable for high school students learning trigonometry and geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, b) → E, F
  4. Rotate(F, (o * π / 180), A) → B
  5. Ray(A, B) → a
  6. OrthogonalLine(B, b) → d
  7. Intersect(b, d) → C
  8. Intersect(b, xAxis) → D
  9. Line(F, d) → e
  10. Angle(b, a) → θ
  11. Segment(A, B) → f
  12. Angle(B, C, A) → α
  13. Segment(A, C) → g
  14. Segment(C, B) → h
  15. Intersect(e, a) → G
  16. Segment(F, G) → i
  17. Angle(G, F, A) → β
  18. Line(G, b) → j
  19. Segment(A, G) → l
  20. Point(c) → H
  21. Segment(A, H) → radius
  22. OrthogonalLine(I, e) → m
  23. Intersect(m, a) → J
  24. Segment(I, J) → n
  25. Angle(J, I, A) → γ
  26. Angle(I, J, A) → δ
  27. OrthogonalLine(J, a) → p
  28. Line(A, p) → q
  29. Point(q) → L
  30. OrthogonalLine(L, q) → s
  31. Intersect(p, s) → M
  32. Segment(L, M) → t
  33. Angle(J, M, L) → ε
  34. Angle(M, L, A) → ζ
  35. Angle(A, J, M) → η
  36. Segment(J, M) → r
  37. Segment(A, L) → f_1