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Cosine Graph from Unit Circle

Cosine Graph from Unit Circle
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2019-06-19 12:08
CircleFunctionTrigonometryCoordinate GeometryGraphing
This example demonstrates how to draw the cosine curve using a unit circle with a vertical y-axis. Key math concepts include the unit circle, cosine function, trigonometric relationships, and analytical geometry. GeoGebra commands and objects used in the construction are Segment, Angle, CurveCartesian, Vector, Rotate, and Sequence. It is suitable for high school students learning to plot trigonometric function graphs and for introductory calculus education.

GeoGebra Commands & Parameters

  1. Segment(A, P) → f
  2. Segment(A, B) → g
  3. Angle(P, A, B) → α
  4. Segment(P, Q) → i
  5. Segment(R, Q) → j
  6. Segment(A, C) → h
  7. CurveCartesian((cos(t), (-t)), t, 0, θ) → a
  8. Vector(A - (1.5, 0), A + (1.5, 0)) → w
  9. Vector((0, 0.3), (0, 3)) → u
  10. Angle(P, A, B) → β
  11. Rotate(eq1, γ, D) → eq1'
  12. Rotate(A, γ, D) → A'
  13. Rotate(P, γ, D) → P'
  14. Segment(A', P') → f'
  15. Rotate(P, γ, D) → P'_1
  16. Rotate(Q, γ, D) → Q'
  17. Segment(P'_1, Q') → i'
  18. Rotate(R, γ, D) → R'
  19. Rotate(Q, γ, D) → Q'_1
  20. Rotate(A, γ, D) → A'_1
  21. Rotate(C, γ, D) → C'
  22. Segment(A'_1, C') → h'
  23. Vector(D, W) → v
  24. Rotate(v, γ, D) → v'
  25. Rotate(R, γ, D) → R'_1
  26. Rotate(Q, γ, D) → Q'_2
  27. Segment(R'_1, Q'_2) → j'_1
  28. Rotate(a, γ, D) → a'_1
  29. Rotate(E, γ, D) → E'
  30. Rotate(F, γ, D) → F'
  31. Vector(E', F') → c
  32. Rotate(G, γ, D) → G'
  33. Rotate(H, γ, D) → H'
  34. Vector(G', H') → d
  35. Rotate(I, γ, D) → I'
  36. Rotate(J, γ, D) → J'
  37. Vector(I', J') → b
  38. Rotate(L, γ, D) → L'
  39. Rotate(M, γ, D) → M'
  40. Rotate(N, γ, D) → N'
  41. Rotate(O, γ, D) → O'
  42. Rotate(S, γ, D) → S'
  43. Rotate(T, γ, D) → T'
  44. Rotate(U, γ, D) → U'
  45. Rotate(V, γ, D) → V'
  46. Rotate(U, γ, D) → U'_1
  47. Sequence(Segment[(-0.05, ((-π) * i / 2)), (0, ((-π) * i / 2))], i, 1, 4) → l1
  48. Rotate(l1, γ, D) → l1'
  49. Sequence(Segment[(-1 + i, 0.05), (-1 + i, 0)], i, 0, 2, 0.5) → l2
  50. Rotate(l2, γ, D) → l2'
  51. Rotate(B, γ, D) → B'
  52. Angle(B', A', P') → δ
  53. Angle(B', A', P') → ε
  54. Rotate(W, γ, D) → W'
  55. Rotate(Z, γ, D) → Z'
  56. Rotate(A_1, γ, D) → C_1
  57. Rotate(B_1, γ, D) → D_1