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Angle-Cosine-Parabola Animation

Angle-Cosine-Parabola Animation
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2017-01-30 10:25
AngleFunctionCoordinate GeometryGeometric Construction
This example demonstrates the relationship between angles, cosine values, and parabolas through animation, showcasing the integration of geometry and algebra. Key math concepts include angle measurement, cosine function, parabola equations, median line, and pyramid geometry. Construction highlights the use of GeoGebra commands like CurveCartesian, Segment, Circle, Intersect, CircleArc, Angle, Ray, Vector, and Mirror. Ideal for high school mathematics education to understand function graphs, geometric transformations, and dynamic geometric phenomena.

GeoGebra Commands & Parameters

  1. CurveCartesian(((a * t) * cos(t)), ((a * t) * sin(t)), t, 0, (6 * π)) → c
  2. CurveCartesian(x(A), y(A), w, 0, (6 * π)) → b
  3. Segment(B, A) → g
  4. Circle(B, g) → d
  5. Intersect(d, y = 0) → C, D
  6. CircleArc(B, D, A) → e
  7. Angle(D, B, A) → α
  8. CurveCartesian(((a * t) * cos(t)), ((a * t) * sin(t)), t, 0, w) → h
  9. Circle(B, (1.25 * g)) → k
  10. Ray(B, A) → l
  11. Intersect(k, l, 1) → E
  12. Vector(B, E) → u
  13. Intersect(k, y = 0) → F, G
  14. Vector(B, G) → v_1
  15. Mirror(h, y = 0) → h'
  16. Mirror(E, y = 0) → E'
  17. Vector(B, E') → v
  18. Vector(B, H) → q