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Unit Circle with Exact Values (Radians)

Unit Circle with Exact Values (Radians)
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2016-05-14 10:32
CircleTrigonometryGeometric Construction
This example demonstrates the exact values of the unit circle at different radian measures. Key mathematical concepts include trigonometric functions and radian measure. Using GeoGebra commands such as Intersect, Point, and Circle, the construction of the unit circle and its values at various angles are showcased. Suitable for high school mathematics education and learning.

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 centered at the origin with radius 1. Place a point on the circle and connect it to the center with a radius segment. Drop perpendiculars from this point to the x-axis and y-axis, forming a right triangle. Mark several special angle points on the circle, drawing segments from the center to these points and perpendicular segments from them to the axes. Outside the circle, label the trigonometric values for these angles, connecting the center to these labels with segments. Finally, construct a polygon using the point, its x-axis foot, and the center, and also a symmetric polygon based on absolute coordinate values.
The prompt above was compiled from the original drawing commands and is for reference only.