MathPlotAI Logo MathPlotAI

Key Angles in the Unit Circle

Key Angles in the Unit Circle
Loading the math board and drawing, please wait…
2016-03-25 03:18
CircleAngleTrigonometryGeometric ConstructionSlider Animation
This example demonstrates the geometric representation and properties of key angles in the unit circle. It involves core mathematical concepts such as angles, circles, unit circles, line segments, orthocenters, and trigonometric functions. The construction highlights GeoGebra commands like Rotate, Point, Angle, Arc, Segment, Polygon, LineBisector, Midpoint, Intersect, and Vector. It is suitable for high school mathematics education, aiding in understanding the relationship between trigonometric functions and the unit circle, as well as geometric constructions.

GeoGebra Commands & Parameters

  1. Rotate(Pi0, 1.5707963267948966) → Pi1Over2
  2. Rotate(Pi0, 1.0472) → Pi1Over3
  3. Rotate(Pi0, 0.7854) → Pi1Over4
  4. Rotate(Pi0, 0.5236) → Pi1Over6
  5. Rotate(Pi0, 2.0943951023931953) → Pi2Over3
  6. Rotate(Pi0, 2.356194490192345) → Pi3Over4
  7. Rotate(Pi0, 2.617993877991494) → Pi5Over6
  8. Rotate(Pi0, 3.141592653589793) → Pi1Over1
  9. Rotate(Pi0, 3.665191429188092) → Pi7Over6
  10. Rotate(Pi0, 3.9269908169872414) → Pi5Over4
  11. Rotate(Pi0, 4.1887902047863905) → Pi4Over3
  12. Rotate(Pi0, 4.71238898038469) → Pi3Over2
  13. Rotate(Pi0, 5.235987755982988) → Pi5Over3
  14. Rotate(Pi0, 5.497787143782138) → Pi7Over4
  15. Rotate(Pi0, 5.759586531581287) → Pi11Over6
  16. Point(unitCircle) → T
  17. Angle(T) → theta
  18. Arc(unitCircle, Pi0, T) → arcTheta
  19. Point(unitCircle) → A
  20. Segment(O, A) → OA
  21. Angle(A, O, Pi1Over3) → AOT
  22. Angle(O, T, A) → OTA2
  23. Segment(A, T) → AT2
  24. Polygon(T1, T2, 3) → poly1, a, b, e, T3
  25. LineBisector(a) → c
  26. Midpoint(T1, T2) → B
  27. Segment(T3, B) → d
  28. Intersect(d, a) → C
  29. Angle(T3, C, T1) → α
  30. Angle(T2, C, T3) → β
  31. Angle(T2, T1, T3) → γ
  32. Segment(A, Pi1Over3) → AT
  33. Segment(O, Pi1Over3) → OT
  34. Midpoint(OA) → B2
  35. Polygon(O, B2, Pi1Over3) → costriangle, pi1over3, o, b2
  36. Angle(T3, T2, T1) → δ
  37. Vector(Midpoint[Corner[text1, 1], Corner[text1, 2]], Midpoint[d]) → sinvector