Unit Circle with Tangent Line

Unit Circle with Tangent Line
Loading the math board and drawing, please wait…
2018-12-19 05:01
This example demonstrates the tangent line to a point on the unit circle and its related geometric properties. Core math concepts include the unit circle, tangent line, angle, orthogonal line, and analytical geometry. Construction highlights involve GeoGebra commands/objects like Point, Ray, Angle, OrthogonalLine, Intersect, Segment, CircleArc, Line, If, AnimationState, and ControlText. Suitable for high school students learning trigonometry, derivatives, and geometric constructions.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Ray(O, P) → a
  3. Angle(C, O, P) → θ
  4. OrthogonalLine(P, b) → e
  5. OrthogonalLine(P, d) → f
  6. Intersect(d, f) → D
  7. Intersect(b, e) → E
  8. Segment(P, E) → g
  9. Segment(D, O) → h
  10. Segment(O, E) → i
  11. OrthogonalLine(C, b) → j
  12. Intersect(c, j, 1) → B
  13. CircleArc(O, B, P) → p
  14. Line(O, P) → l
  15. Intersect(j, l) → T
  16. Segment(C, T) → k
  17. If(AnimationState ≟ 0, "Turn Animation On", "Turn Animation Off") → ControlText