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Exact Values on the Unit Circle (Degrees) by Adam Antonio

Exact Values on the Unit Circle (Degrees) by Adam Antonio
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2016-04-07 05:21
CircleAngleTrigonometryGeometric Construction
This example demonstrates how to mark exact trigonometric values on the unit circle corresponding to specific angles. Key math concepts include the unit circle, angles, trigonometric functions (sine, cosine, tangent), and geometric constructions. It utilizes GeoGebra commands like Intersect, Point, Circle, Segment, Distance, Angle, Vector, and Polygon. Suitable for high school students learning about trigonometric applications and geometric constructions.

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