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Unit Circle Definition of Inverse Trig Functions: arccos

Unit Circle Definition of Inverse Trig Functions: arccos
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2017-02-05 09:12
CircleAngleFunctionTrigonometrySlider Animation
In collections Mapping Diagrams: From AB to C&DE, Resource
This GeoGebra example visualizes the definition of the inverse cosine function (arccos) on the unit circle, showing how the angle relates to the x-coordinate of a point on the circle. It demonstrates the geometric meaning of inverse trigonometric functions, emphasizing the relationship between angles, coordinates, and the principal value range. The construction uses commands such as Point, Circle, Intersect, Angle, Segment, OrthogonalLine, Sequence, Vector, Line, Ray, and CircleArc, along with objects like sliders and text labels to dynamically illustrate the concept. It is suitable for high school or introductory college students learning inverse trigonometry, and serves as an interactive teaching aid for understanding domain, range, and the graphical representation of arccos.

GeoGebra Commands & Parameters

  1. Point(xAxis) → N
  2. Point(yAxis) → D
  3. Intersect(xAxis, yAxis) → A
  4. Circle(A, B) → c
  5. Segment(A, C) → a
  6. Segment(B, A) → b
  7. Angle(B, A, C) → α
  8. OrthogonalLine(C, yAxis) → d
  9. Segment(D, A) → h
  10. Segment(H, B) → i
  11. Sequence((-1.5, t), t, -87.96459430051421, 87.96459430051421, 0.2617993877991494) → tval
  12. Vector(C, K) → j
  13. Vector(A, L) → k
  14. Segment(B, L) → l
  15. Line(L, B) → n
  16. Segment(T_0, t_2) → p
  17. Ray(A, B) → q
  18. Ray(A, C) → r
  19. CircleArc(A, B, C) → e
  20. Vector(C, t_2) → w_2
  21. Vector(D, C) → u_3
  22. CircleArc(A, C, B) → s
  23. Angle(C, A, B) → β
  24. Vector(F, E) → v_2
  25. OrthogonalLine(N, i) → c_1
  26. Intersect(e, c, 1) → O
  27. Vector(N, O) → u
  28. Intersect(c, c_1, 2) → P
  29. Vector(N, P) → v
  30. CircleArc(A, B, P) → d_1
  31. Vector(P, Q) → w
  32. Angle(B, A, P) → γ
  33. Ray(A, P) → e_1
  34. Point(f_1) → R
  35. Segment(R, A) → g_1
  36. Intersect(c, d_1) → S, , ,
  37. Intersect(c, g_1) → T,
  38. CircleArc(A, B, T) → h_1
  39. Vector(R, T) → u_1
  40. Angle(B, A, T) → δ
  41. Angle(B, A, T) → ε
  42. Vector(T, U) → v_1
  43. Segment(A, P) → j_1
  44. Segment(T_0, Q) → k_1
  45. CircleArc(A, B, T) → p_1
  46. Vector(V, W) → w_1
  47. Vector(W, J) → z
  48. Vector(W, M) → m
  49. Sequence((0, k), k, -1, 1, 0.5) → list1
  50. Sequence((1, k), k, -1, 1, 0.5) → list2
  51. Sequence((2, k), k, -1, 1, 0.5) → list3