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1 Radian: Clear Definition

1 Radian: Clear Definition
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2015-11-23 04:05
AngleTrigonometryCalculusGeometric Construction
In collections Geometry Review GA Chapter 8: Right Triangles and Trigonometry Unit Circle and Radian Defining Geometry Applets
This example dynamically demonstrates the definition of 1 radian, illustrating the central angle subtended by an arc equal to the radius on a circle. Key math concepts include radian measure, the relationship between angles and arc lengths, and properties of circles. GeoGebra commands like Center, Rotate, Angle, CircleArc, Dilate, Segment, and Point are used to construct the circle, arc, angle, and their relationships. Suitable for high school students learning radian measure and its application in calculus, particularly arc length and angle conversion.

GeoGebra Commands & Parameters

  1. Center(c) → B
  2. Rotate(A, 1, B) → A'
  3. Angle(A, B, A') → α
  4. Rotate(A', 1, B) → A''
  5. Angle(A', B, A'') → β
  6. Rotate(A'', 1, B) → A'''
  7. Angle(A'', B, A''') → γ
  8. Rotate(A''', 1, B) → C
  9. Angle(A''', B, C) → δ
  10. Rotate(C, 1, B) → C'
  11. Angle(C, B, C') → ε
  12. Rotate(C', 1, B) → C''
  13. Angle(C', B, C'') → ζ
  14. CircleArc(B, A, A') → d
  15. CircleArc(B, A', A'') → e
  16. CircleArc(B, A'', A''') → f
  17. CircleArc(B, A''', C) → g
  18. CircleArc(B, C, C') → h
  19. CircleArc(B, C', C'') → k
  20. Rotate(A, If[0 ≤ a ≤ 1, (a * α), α], B) → A'_1
  21. CircleArc(B, A, A'_1) → p
  22. Dilate(B, If[0 ≤ a ≤ 1, 1 - a, 0], A) → B'
  23. Segment(B', A) → b
  24. CircleArc(B, C'', A) → q
  25. CircleArc(B, A'_1, A') → s
  26. Segment(B, B') → j
  27. Segment(B, A') → l
  28. Point(h) → D
  29. Segment(B, D) → Radius