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Cosine & Unit Circle - Radians

Cosine & Unit Circle - Radians
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2014-01-06 18:21
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
In collections Trigonometry: Basic and More
This example demonstrates the relationship between the cosine function value and the corresponding angle in radians on the unit circle. Key math concepts include cosine function, unit circle, radian measure, and trigonometric values. Construction highlights GeoGebra commands like Line, Circle, Intersect, Rotate, OrthogonalLine, Angle, Segment, Distance, Midpoint, Point, and CircleArc. Suitable for high school mathematics education to help students understand the connection between radian measure and trigonometric function values, deepening their comprehension of trigonometric concepts.

GeoGebra Commands & Parameters

  1. Line(B, O) → a
  2. Circle(O, 1) → c
  3. Intersect(c, a, 2) → C
  4. Rotate(C, α, O) → D
  5. OrthogonalLine(D, a) → e
  6. Intersect(a, e) → A
  7. Angle(C, O, D) → β
  8. Segment(O, D) → b
  9. Distance(D, a) → d
  10. Segment(A_1, D_1) → h
  11. Midpoint(O, A) → E
  12. Midpoint(A_1, D_1) → F
  13. Point(xAxis) → G
  14. Segment(G, A_1) → i
  15. Intersect(c, a, 2) → H
  16. Intersect(c, a, 1) → I
  17. Segment(I, H) → j
  18. CircleArc(O, J, D) → k
  19. Segment(A, O) → l
  20. Segment(O, A) → g
  21. Segment(A, D) → m