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Definition of Arctangent on Unit Circle

Definition of Arctangent on Unit Circle
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2017-02-05 09:17
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Mapping Diagrams: From AB to C&DE, Resource
This example demonstrates the definition of the arctangent function on the unit circle, illustrating the relationship between an angle and the ratio of the opposite side to the adjacent side in a right triangle. Key math concepts include the unit circle, trigonometric functions, arctangent function, and similarity of right triangles. Construction involves commands like Point, Intersect, Circle, Segment, OrthogonalLine, Sequence, Vector, Line, Ray, CircleArc, Angle. Suitable for high school students learning the geometric meaning and definition of the arctangent function.

GeoGebra Commands & Parameters

  1. Point(f_1) → R
  2. Point(xAxis) → N
  3. Point(yAxis) → D
  4. Intersect(xAxis, yAxis) → A
  5. Circle(A, B) → c
  6. Segment(A, C) → a
  7. Segment(B, A) → b
  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. Vector(F, E) → v_2
  24. OrthogonalLine(N, i) → c_1
  25. Intersect(e, c, 1) → O
  26. Vector(N, O) → u
  27. Intersect(c, c_1, 2) → P
  28. Vector(N, P) → v
  29. CircleArc(A, B, P) → d_1
  30. Vector(P, Q) → w
  31. Ray(A, P) → e_1
  32. Segment(R, A) → g_1
  33. Intersect(c, d_1) → S, , ,
  34. Intersect(c, g_1) → T,
  35. CircleArc(A, B, T) → h_1
  36. Vector(R, T) → u_1
  37. Angle(B, A, T) → ε
  38. Vector(T, U) → v_1
  39. Segment(A, P) → j_1
  40. Segment(T_0, Q) → k_1
  41. CircleArc(A, B, T) → p_1
  42. Vector(V, W) → w_1
  43. Vector(W, J) → z
  44. Vector(W, M) → m
  45. Sequence((0, k), k, -1, 1, 0.5) → list1
  46. Sequence((1, k), k, -1, 1, 0.5) → list2
  47. Sequence((2, k), k, -1, 1, 0.5) → list3
  48. CircleArc(A, T, B) → q_1
  49. Angle(T, A, B) → δ