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Coterminal Angles Dynamic Demonstration

Coterminal Angles Dynamic Demonstration
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2017-02-05 11:04
AngleVectorGeometric Construction
In collections Trigonometric Functions of Angles
This example demonstrates the dynamic changes of coterminal angles, involving the concept of angles. Using GeoGebra commands such as CurveCartesian, Segment, Circle, etc., the angle can be dynamically modified to observe the changes of coterminal angles. Suitable for high school math education.

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(E, y = 0) → E'
  16. Vector(B, E') → v
  17. Vector(B, H) → q
  18. Circle(B, (15 * a)) → r
  19. Ray(B, I) → t
  20. CurveCartesian(((a * t) * cos(t)), ((a * t) * sin(t)), t, 0, (a_1 * pos)) → b_1
  21. CurveCartesian(((a * t) * cos(t)), ((a * t) * sin(t)), t, 0, pos) → c_1
  22. CurveCartesian(((a * t) * cos(t)), ((a * t) * sin(t)), t, 0, ((a_1 - 1) * neg)) → d_1
  23. Mirror(d_1, y = 0) → e_1
  24. Vector(B, J) → p
  25. Mirror(L, y = 0) → L'
  26. Mirror(M, y = 0) → M'
  27. Vector(B, K) → u_1
  28. Vector(B, L') → w_1

AI Drawing Prompt Reference

Draw a dynamic demonstration of coterminal angles. Start with a ray from the origin as the initial side of an angle. Construct a circle centered at the origin with adjustable radius. Pick a point on the circle, connect it to the origin to form the terminal side, and display the angle measure. Also draw a spiral curve from the origin whose radius increases with angle, and let a portion of the spiral extend dynamically with the angle to show different coterminal angles. Mark the intersection of the terminal side with the circlehol and draw a vector from the origin to that point. Additionally, draw a larger concentric circle outside, mark the intersection of the extended terminal side with it, and draw the corresponding vector. Finally, mirror the spiral about the horizontal axis to show negative coterminal angles.
The prompt above was compiled from the original drawing commands and is for reference only.