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Discover sin(a+b) and cos(a+b) Identities

Discover sin(a+b) and cos(a+b) Identities
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2015-09-21 08:42
AngleFunctionTrigonometry
In collections Trigonometric Identities
This GeoGebra applet guides students through a logical reasoning activity to discover the trigonometric identities for the sine and cosine of the sum of two angles. It involves key concepts such as angles and trigonometric functions. Using commands like Ray, Intersect, OrthogonalLine, students can visually understand the geometric meaning of these identities. Suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Ray(A, C) → a
  2. Ray(A, D) → c
  3. Intersect(a, b) → E
  4. OrthogonalLine(E, a) → d
  5. Angle(B, A, E) → α
  6. Angle(E, A, D) → β
  7. Point(d) → F
  8. Angle(F, E, A) → γ
  9. Rotate(D, α, E) → D'
  10. Intersect(d, c) → G
  11. Line(G, xAxis) → e
  12. Intersect(f, yAxis) → H
  13. Intersect(e, f) → I
  14. Intersect(b, e) → J
  15. Segment(G, E) → g
  16. Segment(I, G) → h
  17. Segment(G, J) → i
  18. Segment(J, E) → j
  19. Segment(E, B) → k
  20. Segment(I, A) → l
  21. Segment(A, E) → m
  22. Segment(A, G) → n
  23. Intersect(b, c) → M
  24. Angle(M, E, G) → δ
  25. Segment(A, B) → q
  26. Angle(I, G, A) → ε
  27. Angle(A, I, G) → ζ
  28. Angle(G, J, E) → η
  29. Angle(E, B, A) → θ