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Unit Circle Tangent by Kevin

Unit Circle Tangent by Kevin
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2017-02-17 01:19
CircleTrigonometryGeometric Construction
This example demonstrates the tangent of a unit circle. Key mathematical concepts include the properties of circles, the definition of tangents, and angle relationships. Using GeoGebra commands such as Point, Rotate, Angle, Segment, etc., it dynamically shows the relationship between the tangent and the circle. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(Ray[(0, 0), (-1, 0)]) → B
  2. Rotate(A, θ, B) → P
  3. Rotate(A, θ, B) → A'
  4. Angle(A, B, A') → α
  5. Rotate(A, θ, B) → A'_1
  6. Angle(A, B, A'_1) → β
  7. Segment(Q, (x(Q), 0)) → e
  8. Segment((0, 0), (x(Q), 0)) → g
  9. Circle(B, A) → c
  10. Segment(B, P) → a
  11. Vector((x(B), y(Corner[1])), (x(B), y(Corner[4]))) → u
  12. Vector((0, y(Corner[1])), (0, y(Corner[4]))) → w
  13. Vector((0, 0), (x(Corner[2]), 0)) → z
  14. Sequence(Segment[((0.75 * i), 0), ((0.75 * i), -0.025)], i, 1, 4) → list1
  15. Segment(B, (x(P), 0)) → b
  16. Segment(P, (x(P), 0)) → h
  17. Function(cos((120° * x)), 0, x(Q)) → f
  18. Vector(B - (1.2, 0), B + (1.2, 0)) → v
  19. Sequence(Segment[(0, (0.5 * i) - 1), (-0.025, (0.5 * i) - 1)], i, 0, 4) → list2
  20. Sequence(Segment[(x(B), (0.5 * i) - 1), (x(B) - 0.025, (0.5 * i) - 1)], i, 0, 4) → list3
  21. Sequence(Segment[B + ((0.5 * i) - 1, 0), B + ((0.5 * i) - 1, -0.025)], i, 0, 4) → list4
  22. Segment(Q, (0, y(Q))) → d
  23. Point(Ray[(0, 0), (-1, 0)]) → B_1
  24. Rotate(A_1, θ, B_1) → P_1
  25. Rotate(A_1, θ, B_1) → A'_2
  26. Rotate(A_1, θ, B_1) → A'_3
  27. Circle(B_1, A_1) → c_1
  28. Segment(B_1, P_1) → a_1