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Triangle Trigonometry and Circle Geometry Demo

Triangle Trigonometry and Circle Geometry Demo
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2017-02-04 05:37
CircleVectorTrigonometrySequenceGeometric Construction
This example dynamically demonstrates the geometric relationship between a triangle's incircle and its sides and angles, visually showcasing the connection between trigonometric functions and circles. Core concepts include trigonometry, incircle, angles, vectors, and sequences. Construction highlights use of GeoGebra commands like Intersect, Point, Circle, Segment, Angle, OrthogonalLine, CircleArc, Vector, Sequence, and Zip. Suitable for high school mathematics education to understand the intrinsic link between trigonometric functions and geometric figures, enhancing spatial reasoning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → E
  3. Circle(A, B) → c
  4. Segment(A, C) → a
  5. Segment(B, A) → b
  6. Angle(B, A, C) → α
  7. OrthogonalLine(C, yAxis) → d
  8. Intersect(d, yAxis) → D
  9. CircleArc(A, B, C) → e
  10. Vector(C, D) → u
  11. Vector(E, F) → v
  12. Segment(D, A) → h
  13. Segment(H, B) → i
  14. Vector(t, C) → w
  15. OrthogonalLine(C, b) → j
  16. Intersect(j, i) → I
  17. Vector(C, I) → z
  18. Vector(E, K) → l
  19. Sequence(n, n, -10, 10) → k
  20. Zip((0, (((4 * j) + 1) * π / 2)), j, k) → sinmaxl
  21. Zip((0, (((4 * j) - 1) * π / 2)), j, k) → sinminl
  22. Zip(Segment[(0, (((4 * j) - 1) * π / 2)), (0, (((4 * j) + 1) * π / 2))], j, k) → sinincl
  23. Zip(Segment[(0, (((4 * j) + 1) * π / 2)), (0, (((4 * j) + 3) * π / 2))], j, k) → sindecl
  24. Zip(Segment[(-1.5, (((4 * j) - 1) * π / 2)), (-1.5, (((4 * j) + 1) * π / 2))], j, k) → sininclcir
  25. Zip(Segment[(-1.5, (((4 * j) + 1) * π / 2)), (-1.5, (((4 * j) + 3) * π / 2))], j, k) → sindeclcir
  26. Vector(I, J) → m
  27. Zip((0, ((2 * j) * π)), j, k) → cosmaxl
  28. Zip((0, (((2 * j) - 1) * π)), j, k) → cosminl
  29. Zip(Segment[(0, (((2 * j) - 1) * π)), (0, ((2 * j) * π))], j, k) → cosincl
  30. Zip(Segment[(0, ((2 * j) * π)), (0, (((2 * j) + 1) * π))], j, k) → cosdecl
  31. Zip(Segment[(-1.5, (((2 * j) - 1) * π)), (-1.5, ((2 * j) * π))], j, k) → cosinclcir
  32. Zip(Segment[(-1.5, ((2 * j) * π)), (-1.5, (((2 * j) + 1) * π))], j, k) → cosdeclcir