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Sin, Cos and Tan Animation from the Unit Circle

Sin, Cos and Tan Animation from the Unit Circle
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2014-11-12 22:46
CircleTrigonometry
This example demonstrates the definitions of sine, cosine, and tangent functions using the unit circle. It involves key concepts such as angles, rotation, and segments. Using GeoGebra commands like Intersect, Rotate, Angle, Line, OrthogonalLine, and Segment, the dynamic changes of these functions with respect to the angle can be observed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c_1
  3. Point(xAxis) → B
  4. Rotate(B, θ°, A) → B'
  5. Angle(B, A, B') → α
  6. Intersect(xAxis, yAxis) → O
  7. Line(O, B') → a
  8. Intersect(c_1, a, 2) → P
  9. OrthogonalLine(P, xAxis) → b
  10. Intersect(b, xAxis) → E
  11. Segment(P, E) → d
  12. OrthogonalLine(S, xAxis) → e
  13. Intersect(e, xAxis) → F
  14. Segment(S, F) → f
  15. OrthogonalLine(C, xAxis) → g
  16. Intersect(g, xAxis) → G
  17. Segment(C, G) → h
  18. OrthogonalLine(P, yAxis) → i
  19. Intersect(i, yAxis) → H
  20. Segment(H, P) → j
  21. Intersect(c_1, xAxis, 2) → I
  22. OrthogonalLine(I, xAxis) → k
  23. Intersect(a, k) → J
  24. Segment(J, I) → l
  25. Segment(A, J) → m
  26. OrthogonalLine(D, xAxis) → n
  27. Intersect(n, xAxis) → K
  28. Segment(D, K) → p
  29. Segment(A, P) → q

AI Drawing Prompt Reference

Draw a unit circle and rotate a point on it to observe the angle α between the line connecting the point and the origin, and the intersection point E of the perpendicular line from P to the x-axis, the intersection point P of the perpendicular line from the point to the circle, and the intersection point F of the perpendicular line from P to the x-axis, to represent the sine, cosine, and tangent functions.
The prompt above was compiled from the original drawing commands and is for reference only.