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Radians to Revolutions

Radians to Revolutions
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2015-11-25 02:27
AngleTrigonometryGeometric Construction
In collections Geometry Review GA Chapter 8: Right Triangles and Trigonometry
This applet illustrates that 2π radians equal one full revolution. Key mathematical concepts include radian measure and rotation angles. Using GeoGebra commands like Rotate, Angle, and CircleArc, students can visually understand the relationship between radians and rotations. Suitable for middle school and above students learning geometry and trigonometry.

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
  30. Rotate(B', If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → B''
  31. Rotate(d, If[1.2 ≤ a ≤ 2.2, ((a - 1.2) * β), β], B) → d'
  32. CircleArc(B, A, B'') → t
  33. Dilate(B, If[1.2 ≤ a ≤ 2.2, 2.2 - a, 0], A) → B'_1
  34. Segment(B'_1, A) → m
  35. Segment(B, B'_1) → n
  36. Dilate(B, If[2.4 ≤ a ≤ 3.4, 3.4 - a, 0], A) → B'_2
  37. Segment(B, B'_2) → a_1
  38. Segment(B'_2, A) → b_1
  39. Rotate(d', If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → d''
  40. Rotate(t, If[2.4 ≤ a ≤ 3.4, ((a - 2.4) * β), β], B) → t'
  41. Rotate(A, If[2.4 < a < 3.4, ((a - 2.4) * β), β], B) → A'_2
  42. CircleArc(B, A, A'_2) → c_1
  43. Dilate(B, If[3.6 ≤ a ≤ 4.6, 4.6 - a, 0], A) → B'_3
  44. Segment(B'_3, A) → d_1
  45. Segment(B, B'_3) → e_1
  46. Rotate(A, If[3.6 < a < 4.6, ((a - 3.6) * β), β], B) → A'_3
  47. CircleArc(B, A, A'_3) → f_1
  48. Rotate(d'', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → d'''
  49. Rotate(t', If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → t''
  50. Rotate(c_1, If[3.6 ≤ a ≤ 4.6, ((a - 3.6) * β), β], B) → g_1
  51. Dilate(B, If[4.8 ≤ a ≤ 5.8, 5.8 - a, 0], A) → B'_4
  52. Segment(B, B'_4) → h_1
  53. Segment(B'_4, A) → i_1
  54. Rotate(d''', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → k_1
  55. Rotate(t'', If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → t'''
  56. Rotate(g_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → p_1
  57. Rotate(f_1, If[4.8 ≤ a ≤ 5.8, ((a - 4.8) * β), β], B) → q_1
  58. Rotate(A, If[4.8 < a < 5.8, ((a - 4.8) * β), β], B) → A'_4
  59. CircleArc(B, A, A'_4) → r_1
  60. Dilate(B, If[6 ≤ a ≤ 7, 7 - a, 0], A) → B'_5
  61. Segment(B'_5, A) → j_1
  62. Segment(B, B'_5) → l_1
  63. Rotate(A, If[6 < a < 7, ((a - 6) * β), β], B) → A'_5
  64. CircleArc(B, A, A'_5) → s_1
  65. Rotate(k_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → t_1
  66. Rotate(t''', If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → c_2
  67. Rotate(p_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → d_2
  68. Rotate(q_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → e_2
  69. Rotate(r_1, If[6 ≤ a ≤ 7, ((a - 6) * β), β], B) → f_2
  70. CircleArc(B, C'', A) → g_2

AI Drawing Prompt Reference

Draw a circle centered at point B and a unit arc d starting from B. Then rotate around B with A as the starting point and angle α to draw arc d'. Next, rotate around B with A' as the starting point and angle β to draw arc t. Finally, rotate around B with A'' as the starting point and angle γ to draw arc t'.
The prompt above was compiled from the original drawing commands and is for reference only.