Unit Circle and Tangent Function Demo

Unit Circle and Tangent Function Demo
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2012-06-08 21:57
① This example dynamically shows the correspondence between an angle on the unit circle and its tangent value; the y‑coordinate of the green segment equals the tangent of the angle. ② Core mathematical concepts: unit circle, trigonometric functions (sine, cosine, tangent), angle measurement in radians and degrees, and the graph of the tangent function in coordinate geometry. ③ Construction highlights: Point and Circle create the unit circle and a movable point; Intersect, Rotate, and Angle define the angle; Segment, OrthogonalLine, Tangent, Line, and Ray build the tangent line and its projection to display the tangent value in real time. ④ Suitable for high‑school trigonometry lessons, college pre‑calculus introductions, and interactive GeoGebra teaching materials.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, α, A) → P
  5. Angle(B, A, P) → β
  6. Segment(A, P) → a
  7. OrthogonalLine(P, xAxis) → b
  8. Tangent(B, c) → d,
  9. Line(A, P) → e
  10. Intersect(e, d) → D
  11. Segment(B, D) → h
  12. Ray(H, U) → q
  13. Ray(I, V) → r
  14. Segment(J, K) → s
  15. Segment(K, O) → t
  16. Segment(K, Q) → a_1
  17. Segment(M, A_1) → b_1
  18. Segment(M, B_1) → c_1
  19. Segment(J, C_1) → d_1
  20. Segment(J, D_1) → e_1
  21. Segment(L, N) → f_1
  22. Segment(L, E) → g_1
  23. Segment(M, M') → h_1
  24. Line(V, U) → l
  25. Line(X, W) → m
  26. Line(Z, Y) → n
  27. Line(G, F) → p

AI Drawing Prompt Reference

Show a unit circle with a movable point, an angle rotating from that point to another, and a green segment whose y-coordinate equals the tangent of the angle. Draw a tangent line that intersects the unit circle at the angle's point, and its intersection with the x-axis reflects the tangent value. The diagram dynamically displays the relationship between the angle and its tangent, suitable for learning trigonometry and geometric constructions.
The prompt above was compiled from the original drawing commands and is for reference only.