Angle Orientations (Standard Position) - Dynamic & Modifiable Illustrator

Angle Orientations (Standard Position) - Dynamic & Modifiable Illustrator
Loading the math board and drawing, please wait…
2017-01-30 09:12
① This example dynamically illustrates how positive and negative angles are drawn in standard position (vertex at origin, initial side along positive x-axis), with an interactive and modifiable interface. ② Core math concepts include standard position of angles, orientation (counterclockwise for positive, clockwise for negative), and dynamic angle measurement. ③ Construction uses GeoGebra commands such as CurveCartesian, Segment, Circle, Intersect, CircleArc, Angle, Ray, Vector, and Mirror; objects include points (A, B, C, D, E, etc.), segments, circles, angle α, and a button (button1) for interactive modification. ④ Suitable for middle and high school students learning angle concepts, introductory trigonometry, or geometry; also useful for teachers demonstrating angle orientation in class or for students exploring angle direction and magnitude independently.

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