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Unit Circle by Taylor

Unit Circle by Taylor
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2013-03-30 01:49
CircleTrigonometryCoordinate Geometry
In collections The Unit Circle Begins
This example demonstrates the geometric construction of the unit circle. Key mathematical concepts include the properties of circles, angles, and trigonometric functions. Using GeoGebra commands such as Point, Segment, and Polygon, the example dynamically shows points on the unit circle, angles, and trigonometric values. Suitable for students in middle school and above learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Sequence((π * k) / 12, k, 0, 24) → Angles
  3. Sequence((cos(Element[Angles306090, k]), sin(Element[Angles306090, k])), k, 1, 9) → Pts306090
  4. Segment(O, B) → d
  5. Min(abs(Angles306090 - acos(x(A)))) → d306090
  6. Min(abs(Angles459045 - acos(x(A)))) → d459045
  7. Min(abs(AnglesVH - acos(x(A)))) → dVH
  8. If((d306090 ≤ d459045) ∧ (d306090 ≤ dVH), 1, 0) → is306090
  9. If((d459045 < d306090) ∧ (d459045 < dVH), 1, 0) → is459045
  10. If((dVH < d306090) ∧ (dVH < d459045), 1, 0) → isVH
  11. If(y(A) > 0, acos(x(A)), π + acos(-x(A))) → theta
  12. Polygon(O, A, B) → Triangle306090, b, o, a
  13. Polygon(O, A, B) → Triangle459045, b_1, o_1, a_1
  14. Polygon(O, A, B) → TriangleVH, b_2, o_2, a_2
  15. Sequence((cos(Element[Angles459045, k]), sin(Element[Angles459045, k])), k, 1, 4) → Pts459045
  16. Sequence((cos(Element[AnglesVH, k]), sin(Element[AnglesVH, k])), k, 1, 4) → PtsVH
  17. Sequence((cos(Element[AnglesAll, k]), sin(Element[AnglesAll, k])), k, 1, Length[AnglesAll]) → PtsAll
  18. Element(AnglesAllLabels, 2) → Fail
  19. Random(1, 14) → randInt
  20. If(theta > π, "-", "") → negSin
  21. If((π / 2 < theta) ∧ (theta < (3 * π) / 2), "-", "") → negCos
  22. If(tan(theta) < 0, "-", "") → negTan
  23. Angle(O2, O, A) → alphaGreen
  24. If(theta ≟ π / 3 ∨ theta ≟ 2 * π / 3 ∨ theta ≟ 4 * π / 3 ∨ theta ≟ 5 * π / 3, 1) → isTall306090
  25. If(theta ≟ π / 6 ∨ theta ≟ 5 * π / 6 ∨ theta ≟ 7 * π / 6 ∨ theta ≟ 11 * π / 6, 1) → isSkinny306090
  26. If(theta ≟ π / 4 ∨ theta ≟ 3 * π / 4 ∨ theta ≟ 5 * π / 4 ∨ theta ≟ 7 * π / 4, 1) → isReal459045
  27. If(theta ≟ 0 ∨ theta ≟ π ∨ theta ≟ 2 * π, 1) → isH
  28. Point(xAxis) → C
  29. Point(xAxis) → D
  30. Point(xAxis) → E
  31. Point(xAxis) → F
  32. Point(yAxis) → G
  33. Point(yAxis) → H
  34. Point(yAxis) → I
  35. Point(yAxis) → J
  36. Point(c_1) → A_1
  37. Point(c_2) → A_2
  38. Angle(O2, O, A) → alphaRed
  39. Angle(O2, O, A) → alphaBlue

AI Drawing Prompt Reference

Draw a unit circle with the center O, and mark points P for angles 30°, 60°, 90°, etc., connecting them to O to form triangles. Mark points Q for angles 45°, 90°, 45°, etc., and triangles, and points R for all angles. Mark four points C, D, E, F on the x-axis and four points G, H, I, J on the y-axis.
The prompt above was compiled from the original drawing commands and is for reference only.