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Unit Circle and Sine/Cosine

Unit Circle and Sine/Cosine
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2017-03-21 21:51
CircleTrigonometryGeometric Construction
This example demonstrates the unit circle and sine/cosine functions. Key mathematical concepts include trigonometry, unit circle, and angles. Using GeoGebra commands such as Point, Intersect, Rotate, etc., it dynamically shows the changes in sine and cosine values. Suitable for high school math education and learning.

GeoGebra Commands & Parameters

  1. Point(xAxis) → B
  2. Intersect(xAxis, yAxis) → C
  3. Rotate(B, α, C) → B'
  4. Segment(B, C) → g
  5. FractionText(2 / ar) → p
  6. CircleArc(C, B, B') → d
  7. Textfield(α) → InputBox1
  8. OrthogonalLine(B', xAxis) → f
  9. Intersect(xAxis, f) → A
  10. Polygon(A, C, B') → poly1, Cosine, a, Sine
  11. Point(yAxis) → D
  12. Point(xAxis) → E
  13. Point(yAxis) → F
  14. CircleArc(C, B, D) → e
  15. CircleArc(C, D, E) → h
  16. CircleArc(C, E, F) → k
  17. CircleArc(C, F, B) → q
  18. Ray(C, B') → i
  19. Intersect(e, i) → P,
  20. Intersect(h, i) → H,
  21. Intersect(k, i) → I,
  22. Intersect(q, i) → J,
  23. Angle(J, C, B) → β
  24. Angle(A, C, I) → γ
  25. Angle(H, C, A) → δ
  26. Angle(A, C, P) → ε
  27. Rotate(B, α, C) → B'_1
  28. Angle(B, C, B'_1) → ζ
  29. Midpoint(Sine) → G
  30. Midpoint(C, A) → K

AI Drawing Prompt Reference

Draw a unit circle with its center and intersections with the x and y axes. From the center, draw a ray at an angle α to the x-axis. Find the intersection of this ray with the circle and connect it to the center. Label arcs on the circle showing angles α, β, γ, δ, and ε from the positive x-axis, and mark the foot of the perpendicular from these points to the ray. Finally, draw the inscribed quadrilateral and label its sides with corresponding sine and cosine values.
The prompt above was compiled from the original drawing commands and is for reference only.