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Unit Circle by Julia

Unit Circle by Julia
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2017-11-02 11:32
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the geometric properties and trigonometric relationships of the unit circle. It involves core concepts like circle, angle, vector, trigonometry, and coordinate geometry. Construction uses commands such as Intersect, Point, Circle, Segment, Distance, Angle, Vector, Polygon. Suitable for high school mathematics teaching to understand the definition and geometric meaning of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(xAxis) → E
  3. Circle(O, E) → c_1
  4. Point(c_1) → X
  5. Segment(O, X) → a
  6. Distance(X, A_1) → b
  7. Angle(E, O, X) → α
  8. Segment(A_1, (x(A_1), 0)) → f
  9. Segment(A_2, (x(A_2), 0)) → g
  10. Segment(B_2, B_1) → h
  11. Segment(C_2, C_1) → i
  12. Vector(O, X) → u
  13. Vector(X, (x(X), 0)) → v
  14. Vector(X, (0, y(X))) → w
  15. Point(u) → A
  16. Segment(A, C_2) → e
  17. Segment(A, B_2) → j
  18. Segment(A, A_2) → k
  19. Segment(A, A_3) → l
  20. Segment(A, B_3) → m
  21. Segment(A, C_3) → n
  22. Segment(A, C_4) → p
  23. Segment(A, B_4) → q
  24. Segment(A, A_4) → r
  25. Segment(A, A_1) → s_1
  26. Segment(A, B_1) → t
  27. Segment(A, C_1) → a_1
  28. Polygon(X, (x(X), 0), A) → poly1, a_2, B, b_1
  29. Polygon((abs(x(X)), abs(y(X))), A, (abs(x(X)), 0)) → poly2, d_1, e_1, a_3

AI Drawing Prompt Reference

Draw a unit circle with its center at the origin and mark the intersection with the x-axis. Draw a radius from the center to a point on the circle. Mark the projection of this point on the x-axis and draw a line segment connecting the projection to the point on the circle. Label the angle at the center between the radius and the x-axis. From the point on the circle, draw vectors pointing along the x-axis and y-axis. Extend line segments from this point to the boundaries in all four quadrants. Finally, connect the point on the circle, its projection, and the vector endpoints to form two polygons, illustrating the geometric meaning of trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.