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Cosine of the Sum Angle

Cosine of the Sum Angle
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2019-04-02 23:21
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the cosine of the sum angle. Using trigonometry and coordinate geometry, it shows how to calculate the cosine of a sum angle. Commands like CurveCartesian, Point, Intersect, Segment are used. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), sin(t), t, 0, π / 2) → a
  2. Point(a) → A_1
  3. Point(a) → B
  4. Intersect(xAxis, yAxis) → O
  5. Segment(O, A_1) → f
  6. Segment(O, B) → g
  7. OrthogonalLine(B, f) → h
  8. Intersect(h, f) → A
  9. OrthogonalLine(B, xAxis) → i
  10. OrthogonalLine(A, xAxis) → j
  11. OrthogonalLine(B, j) → k
  12. Intersect(xAxis, i) → E
  13. Intersect(xAxis, j) → F
  14. Intersect(k, j) → G
  15. Segment(B, E) → l
  16. Segment(B, A) → m
  17. Segment(G, F) → n
  18. Segment(B, G) → p
  19. Angle(E, O, A) → α
  20. Angle(A, O, B) → β
  21. Angle(B, A, O) → γ
  22. Polygon(C, I, H) → t1, h_1, c, d
  23. Angle(I, C, H) → δ
  24. Angle(F, O, B) → ε
  25. Line(L, f) → q
  26. Line(L, g) → r
  27. Point(q) → M
  28. Line(M, m) → s
  29. Intersect(r, s) → N
  30. Segment(L, N) → t
  31. Segment(L, M) → b
  32. Segment(M, N) → e
  33. Angle(M, L, N) → ζ
  34. Segment(P, Q) → f_1
  35. Segment(Q, R) → g_1
  36. Segment(S, R) → i_1
  37. Angle(G, A, B) → η
  38. Segment(T, U) → j_1
  39. Segment(T, U) → k_1
  40. Segment(U, V) → l_1
  41. Segment(V, T) → m_1
  42. Angle(U, V, T) → θ
  43. Segment(W, Z) → n_1
  44. Segment(C_1, B_1) → p_1
  45. Segment(Z, C_1) → q_1
  46. Polygon(D_1, E_1, F_1, G_1) → c1, d_1, e_1, r_1, s_1
  47. Point(d_1) → H_1
  48. Vector(H_1, I_1) → u