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Definition of Radian

Definition of Radian
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2016-06-21 02:02
CircleAngleGeometric Construction
In collections Geo&Alg:Area Volume Pythagorean Th. Rate & Accumulation Yr 4 Much&Fast Trig Tools
This example dynamically demonstrates the definition of a radian using a movable circle center and a point on the circle. Key mathematical concepts include circular angles and radians. GeoGebra commands used include Circle, Segment, OrthogonalLine, Rotate, Angle, and CircleArc. Suitable for high school geometry education.

GeoGebra Commands & Parameters

  1. Circle(center, B) → c
  2. Segment(center, B) → radius
  3. OrthogonalLine(B, radius) → g
  4. Rotate(B, 1, center) → B'
  5. Angle(B, center, B') → α
  6. Segment(center, B') → h
  7. CircleArc(center, B, B') → arc
  8. Rotate(B, 2, center) → B'_1
  9. Angle(B, center, B'_1) → β
  10. Rotate(B, 3, center) → B'_2
  11. Angle(B, center, B'_2) → γ
  12. Rotate(B, π, center) → B'_3
  13. Angle(B, center, B'_3) → δ
  14. Segment(center, B'_1) → f
  15. Segment(center, B'_2) → i
  16. Segment(center, B'_3) → j