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Tracing Tangent Ratio in a Unit Circle

Tracing Tangent Ratio in a Unit Circle
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2017-05-18 15:50
CircleFunctionTrigonometryGeometric Construction
This example demonstrates the tracing of the tangent ratio within a unit circle, illustrating the relationship between angles and lengths. Key math concepts include the unit circle, trigonometric functions, tangent definition, and the connection between angles and lengths. GeoGebra commands/objects used are Point, Rotate, Segment, Angle, Circle, Vector, Sequence, and Function. Suitable for high school mathematics education, helping students explore the connection between trigonometric graphs and the unit circle.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Segment(A, Intersect[Line[B, P], x = x(A)]) → h
  4. Segment(P, Intersect[Line[B, P], x = x(A)]) → g
  5. Rotate(A, θ, B) → A'
  6. Angle(A, B, A') → α
  7. Rotate(A, θ, B) → A'_1
  8. Angle(A, B, A'_1) → β
  9. Segment(Q, (x(Q), 0)) → e
  10. Circle(B, A) → c
  11. Segment(B, P) → a
  12. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  13. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  14. Vector((0, 0), (x(Corner[2]), 0)) → z
  15. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  16. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  17. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  18. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  19. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  20. Segment(C, Q) → d
  21. Function(tan((120° * x)), 0, (θ / ((360 * γ)) * 3)) → f
  22. Point(Ray[(0, 0), (-1, 0)]) → B_1
  23. Rotate(A_1, θ, B_1) → P_1
  24. Rotate(A_1, θ, B_1) → A'_2
  25. Rotate(A_1, θ, B_1) → A'_3
  26. Circle(B_1, A_1) → c_1