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Tangent Function Periodicity Demo

Tangent Function Periodicity Demo
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2017-02-05 09:37
FunctionTrigonometryGeometric Construction
In collections Mapping Diagrams: From AB to C&DE, Resource
This example dynamically demonstrates the graph of the tangent function and its periodicity, visually showing the symmetry axes and periodic properties of the tangent function. Core math concepts include trigonometry, periodicity, symmetry axes, unit circle, and analytical geometry. Construction highlights use GeoGebra commands/objects like Intersect (intersection), Point (point), Circle (circle), Segment (segment), Angle (angle), OrthogonalLine (perpendicular line), CircleArc (arc), and Vector (vector). Suitable for high school students learning trigonometric properties and introductory teaching of function periodicity in calculus.

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(I, J) → k
  19. Vector(E, K) → l
  20. Vector(L, F) → m
  21. Vector(L, K) → n
  22. Segment(t, M) → q
  23. Segment(E, L) → r
  24. Segment(S, U) → b_1
  25. Segment(P, Q) → c_1
  26. Segment(R, T) → a_1
  27. Vector(M, V) → p
  28. Vector(A, W) → u_1
  29. Vector(C, W) → v_1
  30. Vector(V, W) → w_1

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with horizontal x-axis and vertical y-axis. Place a point on the y-axis, then draw a segment from the origin to that point, and another segment from that point to a point on the circle, forming an angle. Through the circle point, draw a perpendicular line to the y-axis, intersecting it at a new point, and connect the origin to that intersection with a segment. Use an arc to connect two points on the circle, and add several vectors indicating tangent directions. Outside the circle, sketch the periodic graph of the tangent function, showing its symmetry axes and periodic nature, with segments and vectors marking key points and directions.
The prompt above was compiled from the original drawing commands and is for reference only.