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Unit Circle and Trigonometric Ratios by Ayoub

Unit Circle and Trigonometric Ratios by Ayoub
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2019-03-01 21:17
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the coordinates of a point on the unit circle and the trigonometric ratios of the central angle. It involves core concepts like the unit circle, trigonometric functions, and coordinate geometry. The construction uses GeoGebra commands such as Intersect, Circle, Point, Segment, Rotate, Angle, OrthogonalLine, and Vector. It is suitable for high school mathematics education to help students understand the definition and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, yAxis) → B, C
  4. Intersect(c, xAxis) → D, E
  5. Point(c) → F
  6. Segment(A, F) → a
  7. Rotate(E, 45°, A) → E'
  8. Angle(E, A, E') → β
  9. Rotate(E, 30°, A) → E'_1
  10. Angle(E, A, E'_1) → γ
  11. Rotate(E, 60°, A) → E'_2
  12. Angle(E, A, E'_2) → δ
  13. OrthogonalLine(F, xAxis) → b
  14. Intersect(b, xAxis) → G
  15. Vector(F, G) → u
  16. OrthogonalLine(F, yAxis) → d
  17. Intersect(yAxis, d) → H
  18. Intersect(d, a) → I
  19. Angle(E, A, F) → α
  20. Vector(F, H) → v
  21. Rotate(E, 120°, A) → E'_3
  22. Angle(E, A, E'_3) → ε
  23. Rotate(E, 135°, A) → E'_4
  24. Angle(E, A, E'_4) → ζ
  25. Rotate(E, 150°, A) → E'_5
  26. Angle(E, A, E'_5) → η
  27. Rotate(E, 210°, A) → E'_6
  28. Angle(E, A, E'_6) → θ
  29. Rotate(E, 240°, A) → E'_7
  30. Angle(E, A, E'_7) → ι
  31. Rotate(E, 300°, A) → E'_8
  32. Angle(E, A, E'_8) → κ
  33. Rotate(E, 315°, A) → E'_9
  34. Angle(E, A, E'_9) → λ
  35. Rotate(E, 330°, A) → E'_{10}
  36. Angle(E, A, E'_{10}) → μ
  37. Rotate(E, 225°, A) → E'_{11}
  38. Angle(E, A, E'_{11}) → ν

AI Drawing Prompt Reference

Draw a unit circle and mark its center. Plot a point on the circle, connect the center to this point, and draw a perpendicular line from the point to the x-axis. Rotate a line from the x-axis by 45°, 30°, 60°, etc., and label the angles these lines make with the x-axis. Also, draw vectors from the center to the feet of the perpendiculars and label the angles these vectors make with the x-axis and y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.