MathPlotAI Logo MathPlotAI

Tangent Graph from Unit Circle by krschreck

Tangent Graph from Unit Circle by krschreck
Loading the math board and drawing, please wait…
2015-02-25 14:22
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to draw tangents from a unit circle and their correspondence with the Cartesian coordinate system. Core math concepts include the unit circle, trigonometric functions (tangent), reflection, and analytical geometry. Construction highlights involve commands/objects like Point, Circle, Intersect, Rotate, Angle, Segment, OrthogonalLine, Tangent, Line, Ray. Suitable for high school students learning about the construction of trigonometric function graphs and applications of the unit circle.

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

Draw a unit circle and select a point B on it. Draw the tangent line d at point B, then draw a vertical line b from point A to the x-axis. Draw a line segment a from A to P, then draw a line segment h from B to the intersection D of line b and line d. Finally, draw a ray q from B and a ray r from A that intersects line d at point D.
The prompt above was compiled from the original drawing commands and is for reference only.