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Constructing the Unit Circle by Hand

Constructing the Unit Circle by Hand
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2016-11-03 02:22
CircleTrigonometryGeometric Construction
This example demonstrates the manual construction of a unit circle using GeoGebra interactive commands, exploring its geometric properties and relationship to trigonometric functions. Core concepts include the definition of a circle, coordinate representation, and the link between circular motion and trigonometric ratios. Construction involves key GeoGebra commands such as Intersect, Circle, Vector, OrthogonalLine, and Point, generating points that define the unit circle's structure. Suitable for high school trigonometry, precalculus, or introductory calculus courses seeking a hands-on understanding of radian measure, parametric circular motion, and the geometric origin of sine and cosine.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, B) → c
  3. Vector(A, B) → u
  4. OrthogonalLine(B, xAxis) → a
  5. OrthogonalLine(B, yAxis) → b
  6. Intersect(b, yAxis) → C
  7. Intersect(xAxis, a) → D
  8. Vector(C, B) → v
  9. Vector(D, B) → w
  10. Intersect(c, xAxis, 2) → E
  11. Point(c) → F
  12. Point(c) → G
  13. Point(c) → H
  14. Point(c) → I
  15. Point(c) → J
  16. Intersect(c, yAxis, 2) → K
  17. Point(c) → L
  18. Point(c) → M
  19. Point(c) → N
  20. Point(c) → O
  21. Point(c) → P
  22. Point(c) → Q
  23. Point(c) → R
  24. Point(c) → S
  25. Point(c) → T
  26. Point(c) → U
  27. Point(c) → V
  28. Intersect(c, yAxis, 1) → W
  29. Point(c) → Z
  30. Point(c) → A_1
  31. Point(c) → B_1
  32. Point(c) → C_1
  33. Point(c) → D_1