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Exact Values on the Unit Circle (Radians) by Mirjana Blažević Mandić

Exact Values on the Unit Circle (Radians) by Mirjana Blažević Mandić
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2017-09-11 01:59
CircleTrigonometryGeometric Construction
This example demonstrates the exact values on the unit circle for common angles. Key mathematical concepts include trigonometric functions and radian measure. Using GeoGebra commands such as Intersect, Point, and Circle, the construction of key points and angles on the unit circle is illustrated. 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 the unit circle with key points and angles, including the origin O and point X on the unit circle c_1, the line segment a connecting OX, the vector u from X to O, and the perpendicular line f from X to the x-axis. Construct angle α and the foot of the perpendicular A from X to the x-axis. Draw multiple line segments from A to form polygons, illustrating the sine and cosine values of common angles on the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.