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Exact Values on the Unit Circle (Radians)

Exact Values on the Unit Circle (Radians)
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2018-11-01 12:07
CircleAngleTrigonometryGeometric Construction
This example demonstrates how to plot and calculate the exact trigonometric values (sine, cosine, tangent) for specific angles (e.g., 0°, 30°, 45°, 60°, 90°) on the unit circle. It involves core math concepts like the unit circle, trigonometric functions, angle measurement in radians, and properties of right triangles. The construction uses GeoGebra commands/objects such as Intersect, Point, Circle, Segment, Distance, Angle, Vector, and Polygon. Suitable for high school students learning the geometric interpretation of trigonometric functions on the unit circle, as well as review of coordinate geometry 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