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Circular Functions Visualization

Circular Functions Visualization
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2016-01-07 00:27
CircleFunctionTrigonometry
This example visualizes the definition of circular functions, focusing on sine and cosine. Using GeoGebra commands such as Rotate, Segment, and CircleArc, the relationship between angles and trigonometric values is dynamically demonstrated. Suitable for high school mathematics, particularly in trigonometry and coordinate geometry.

GeoGebra Commands & Parameters

  1. If(moving, 1, 0) → mov
  2. If(moving, 1, 0) → mobile
  3. Rotate(A, α, O) → P
  4. Segment(O, P) → a
  5. Rotate(A, 1.5707963267948966, O) → A'
  6. Rotate(A', 1.5707963267948966, O) → A''
  7. Rotate(A'', 1.5707963267948966, O) → A'''
  8. Segment(A', A''') → b
  9. Segment(A'', A) → d
  10. Segment(C, P) → ss
  11. Segment(O, C) → cc
  12. Segment(B, D) → g
  13. CircleArc(O, A, P) → alpha
  14. Angle(A, O, P) → β
  15. Segment(O', AA) → e
  16. Segment(AA, PSeno) → f
  17. Sequence(O' + (((2 * k) * 3.141592653589793 / n), 0), k, 1 - (mov * floor((((2 * 3.141592653589793) - α) * n / ((2 * 3.141592653589793))))), n - (mov * floor((((2 * 3.141592653589793) - α) * n / ((2 * 3.141592653589793)))))) → LL
  18. Segment(PCoseno, AA) → i
  19. Vector(O, O') → v
  20. Segment(P, C) → j
  21. Line(P, O) → l
  22. Intersect(l, k) → T
  23. Segment(A, T) → m
  24. Segment(P, T) → h
  25. Segment(PTangente, AA) → q
  26. Segment(PPCos, PCoseno) → r
  27. Segment(PPSen, PSeno) → s
  28. Segment(PPTan, PTangente) → t
  29. Sequence(Line[Element[LL, i], Element[LL, i] + (0, 1)], i, 1, n) → LR
  30. Ray(U, U + (1, 0)) → a_1
  31. Ray(U', U' + (1, 0)) → b_1
  32. Function(Translate[sin(x), v], (mobile * (alpha - (2 * 3.141592653589793))) + x(v), alpha + x(v)) → fs
  33. Function(Translate[cos(x), v], (mobile * (alpha - (2 * 3.141592653589793))) + x(v), alpha + x(v)) → fc
  34. Function(Translate[tan(x), v], (mobile * (alpha - (2 * 3.141592653589793))) + x(v), alpha + x(v)) → ft
  35. Polygon(C1, C2, C3, C4) → poly1, c1, c2, c3, c4

AI Drawing Prompt Reference

Draw a unit circle centered at O and move a point P on the circle to demonstrate the relationship between angle α and point P's position. Use rotation and line segments to dynamically illustrate the definitions of sine, cosine, and tangent functions. First, draw circle O and rotate point A to get point P, then draw line segment a from O to P. Next, rotate A to get A', A'', and A''', and draw line segments b, d, ss, cc, and g. Use a circular arc to draw angle β and then rotate and draw line segments to illustrate sine and cosine values. Finally, rotate and draw line segments to illustrate the tangent value.
The prompt above was compiled from the original drawing commands and is for reference only.