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Unit Circle Trigonometry by Sally Booth

Unit Circle Trigonometry by Sally Booth
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2019-03-12 23:20
CircleAngleFunctionTrigonometryGeometric Construction
This example demonstrates the correspondence between angles and trigonometric values (sin, cos) on the unit circle. Core concepts include the unit circle, trigonometric functions, and angle measurement. GeoGebra commands and objects used are Circle, Rotate, Angle, Intersect, OrthogonalLine, Polygon, Ray, with objects like O, c, θ, x, B, δ. Suitable for high school mathematics teaching and student understanding of trigonometric definitions.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Rotate(x_1, θ_1, O) → B_1
  4. Angle(x_1, O, B_1) → δ_1
  5. OrthogonalLine(B_1, xAxis) → f
  6. Intersect(f, xAxis) → C_1
  7. Polygon(O, B_1, C_1) → t1, c_1, o, b
  8. Rotate(x_1, θ_2, O) → B_2
  9. Angle(x_1, O, B_2) → δ_2
  10. OrthogonalLine(B_2, xAxis) → g
  11. Intersect(g, xAxis) → C_2
  12. Polygon(O, B_2, C_2) → t2, c_2, o_1, b_2
  13. Angle(C_1, O, B_1) → ϕ_1
  14. Angle(B_2, O, C_2) → ϕ_2
  15. Rotate(C_1, θ_3, O) → B
  16. Angle(C_1, O, B) → δ_3
  17. Ray(O, B) → h
  18. Intersect(c, h) → B_3,
  19. OrthogonalLine(B_3, xAxis) → i
  20. Intersect(i, xAxis) → C_3
  21. Polygon(O, B_3, C_3) → t3, c_3, o_2, b_3
  22. Angle(C_3, O, B_3) → ϕ_3
  23. Rotate(C_1, θ_4, O) → A
  24. Angle(C_1, O, A) → δ_4
  25. Ray(O, A) → j
  26. Intersect(c, j) → B_4,
  27. OrthogonalLine(B_4, xAxis) → k
  28. Intersect(k, xAxis) → C_4
  29. Polygon(O, B_4, C_4) → t4, c_4, o_3, b_4
  30. Angle(B_4, O, C_4) → ϕ_4