Geometric Proof of Sine and Cosine Sum Formulas

GeoGebra Commands & Parameters

1. Point(xAxis) → A
2. CircleArc(O, A, B) → c
3. Point(c) → C
4. CircleArc(O, C, B) → q
5. Segment(O, C) → a
6. Point(q) → E
7. Segment(E, O) → d
8. OrthogonalLine(E, a) → e
9. Intersect(e, a) → F
10. Angle(E, F, O) → γ
11. Angle(A, O, C) → α
12. Angle(C, O, E) → β
13. OrthogonalLine(F, xAxis) → f
14. OrthogonalLine(E, yAxis) → g
15. Intersect(f, g) → G
16. Intersect(g, yAxis) → H
17. Intersect(f, xAxis) → D
18. OrthogonalLine(E, xAxis) → b
19. Intersect(b, xAxis) → I
20. Segment(E, I) → h
21. Segment(O, D) → i
22. Segment(D, F) → j
23. Angle(G, F, E) → δ
24. Segment(F, G) → k
25. Segment(G, E) → l
26. Segment(E, G) → m
27. Segment(E, H) → n
28. Segment(H, O) → p
29. Angle(G, D, O) → ε
30. Angle(E, G, F) → ζ
31. Angle(O, H, E) → η
32. Segment(O, F) → r
33. Segment(F, E) → s
34. Segment(H, B) → t
35. Segment(D, A) → a_1
36. Rotate(O, (-α), E) → O'
37. Angle(O', E, O) → θ
38. Rotate(H, β, E) → H'
39. Angle(H, E, H') → ι