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Trig Ratios Unit Circle

Trig Ratios Unit Circle
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2018-08-17 00:49
CircleTrigonometryGeometric Construction
This example demonstrates the geometric representation of trigonometric functions on the unit circle. Key mathematical concepts include trigonometry, circle geometry, and the relationship between angles and trigonometric ratios. Construction involves GeoGebra commands such as Point, Sequence, Segment, Min, If, and Polygon to create points, angles, and triangles. Suitable for middle or high school mathematics education to understand basic trigonometric concepts and the application of the unit circle.

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 - acosd(x(A)))) → d306090
  6. Min(abs(Angles459045 - acosd(x(A)))) → d459045
  7. Min(abs(AnglesVH - acosd(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, acosd(x(A)), π + acosd((-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 and mark points at various angles around it. Connect the origin to each point to form radii. For each angle, draw the corresponding sine, cosine, and tangent lines, labeling their lengths. Also, draw reference triangles for each angle, showing the relationships between the angles and trigonometric functions. Finally, mark key points and angles on the coordinate axes to illustrate the connection between trigonometric ratios and the unit circle.
The prompt above was compiled from the original drawing commands and is for reference only.