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Sine Function and Unit Circle Relationship

Sine Function and Unit Circle Relationship
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2015-05-06 04:57
CircleFunctionTrigonometry
This example demonstrates the relationship between the sine function and the unit circle. Key mathematical concepts include the sine function and the unit circle. By constructing a circle, line segments, angles, and other objects, the periodicity of the sine function and the correspondence between points on the unit circle and sine values are illustrated. Commands used include Point, Circle, Segment, Angle, Line, OrthogonalLine, Intersect, Polygon, CircleArc, and Function. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → a
  6. Angle(B, A, C) → α
  7. Line(A, B) → d
  8. OrthogonalLine(A, d) → b
  9. OrthogonalLine(C, b) → e
  10. Intersect(b, e) → D
  11. Segment(A, D) → f
  12. OrthogonalLine(C, d) → g
  13. Intersect(d, g) → E
  14. Polygon(A, E, C) → poly1, c_1, a_1, e_1
  15. CircleArc(A, B, C) → h
  16. Point(d) → F
  17. Point(Circle[F, h]) → G
  18. Segment(F, G) → i
  19. OrthogonalLine(G, d) → j
  20. Intersect(e, j) → H
  21. Function(sin(x), 0.0, 6.283185307179586) → q
  22. Segment(A, D) → k