MathPlotAI Logo MathPlotAI

Dynamic Unit Circle Reference

Dynamic Unit Circle Reference
Loading the math board and drawing, please wait…
2015-01-12 03:53
CircleTrigonometryGeometric Construction
This example demonstrates the dynamic construction of a unit circle reference. Key mathematical concepts include circle, unit circle, integers, conic sections, arithmetic mean, symmetry, and arithmetic. Using GeoGebra commands such as Intersect, Circle, Rotate, Point, etc., a dynamic unit circle can be constructed. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Rotate(B, 30*°, A) → B'
  4. Point(c) → C
  5. Segment(A, C) → a
  6. OrthogonalLine(C, xAxis) → b
  7. Intersect(b, xAxis) → D
  8. Segment(A, D) → d
  9. Segment(C, D) → e
  10. Polygon(A, C, D) → poly1, d_1, a_1, c_1
  11. Angle(B, A, C) → β
  12. LaTeX(β) → ref
  13. LaTeX(f) → text6
  14. LaTeX(sin(β)) → text11
  15. LaTeX(cos(β)) → text12
  16. If(0 < f < π / 2, f, If[π / 2 < f < π, π - f, If[π < f < (3 * π / 2), f - π, If[(3 * π / 2) < f < (2 * π), (2 * π) - f]]]) → Reference
  17. LaTeX(Reference) → text5
  18. LaTeX(α) → text15

AI Drawing Prompt Reference

Draw a unit circle and mark a point on it. From this point, draw a line segment at a 30-degree angle to the positive x-axis. Connect this point to the circle's center to form a triangle. Label the angle in the triangle and display its sine and cosine values next to it. Based on the angle value, indicate the reference position on the circle corresponding to the radian measure and display this value.
The prompt above was compiled from the original drawing commands and is for reference only.