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Tangent Function Visualization with Geometric Construction

Tangent Function Visualization with Geometric Construction
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2023-03-14 04:21
AngleFunctionTrigonometryGeometric ConstructionGraphing
In collections geometriadinamica.es
This GeoGebra example dynamically illustrates the tangent function (tangente) and its relationship with the unit circle, angles, segments, and other geometric elements. Core mathematical concepts include trigonometric functions (tangent, cosine), angle measurement, function graphing, and geometric transformations (rotation, orthogonal lines). The construction uses commands such as OrthogonalLine, Point, Segment, Intersect, Rotate, Line, Circle, Angle, Polygon, and CircleArc, involving numerous objects like points A, B, C, D, E, O, P, Q, F, H, G; lines f, g, a, d, e, b, h, i, j, k, l, n, p, q; circles c, r; angle α; polygons AA, PP; and arcs T1, T2. It is suitable for high school or pre-university students learning trigonometric graphs and geometric construction, and for teachers demonstrating the periodic nature and asymptotes of the tangent function.

GeoGebra Commands & Parameters

  1. OrthogonalLine(A, xAxis) → m
  2. Point(yAxis) → B
  3. OrthogonalLine(B, yAxis) → f
  4. Point(f) → C
  5. Point(f) → D
  6. Segment(C, D) → g
  7. Point(g) → E
  8. Intersect(xAxis, yAxis) → O
  9. Rotate(A, ang, O) → P
  10. Line(P, O) → r
  11. Circle((0, 0), 1) → c
  12. Angle(AA, O, PP) → α
  13. Polygon(P, O, (x(P), 0)) → Q, a, d, e
  14. Intersect(m, r) → H
  15. Segment(F, G) → b
  16. Segment(F, E) → h
  17. Segment(G, H) → i
  18. Segment(O, F) → j
  19. Circle(O, dis) → p
  20. CircleArc(O, AA / 2, PP / 2) → k
  21. Segment(H, O) → n
  22. Segment(H, A) → q
  23. Segment((x(P), 0), O) → l

AI Drawing Prompt Reference

Draw a dynamic tangent function graph, including a unit circle, angles, segments, and geometric elements. The graph should contain a unit circle, an angle, several segments, a triangle, and an arc. The graph should dynamically display the periodic nature and asymptotes of the tangent function.
The prompt above was compiled from the original drawing commands and is for reference only.