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Sin(x) & Unit Circle - Degrees

Sin(x) & Unit Circle - Degrees
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2020-03-05 00:03
CircleAngleFunctionTrigonometryGeometric Construction
This example demonstrates the relationship between an angle α in degrees and the value of sin(α) using the unit circle through an animation. Key math concepts include trigonometric functions, unit circle, angles, and rotation. It is constructed using GeoGebra commands like Circle, Line, Intersect, Rotate, Angle, Segment, Distance, OrthogonalLine, Midpoint, and Point. Suitable for high school students or beginners learning about the connection between trigonometric functions and the unit circle, aiding comprehension and teaching.

GeoGebra Commands & Parameters

  1. Circle(O, 1) → c
  2. Line(B, O) → a
  3. Intersect(c, a, 2) → C
  4. Rotate(C, α, O) → D
  5. Angle(C, O, D) → β
  6. Segment(O, D) → b
  7. Distance(D, a) → d
  8. OrthogonalLine(D, a) → e
  9. Intersect(a, e) → A_2
  10. Segment(D, A_2) → g
  11. Segment(A_1, D_1) → h
  12. Midpoint(D, A_2) → E
  13. Midpoint(A_1, D_1) → F
  14. Point(xAxis) → G
  15. Segment(G, A_1) → i
  16. Intersect(c, a, 2) → A
  17. Intersect(c, a, 1) → I
  18. Segment(I, A) → j
  19. Intersect(c, j, 2) → J
  20. Segment(O, A_2) → l
  21. Midpoint(O, D) → K

AI Drawing Prompt Reference

Draw a unit circle and mark an angle α on it, then rotate to get point D, draw a segment from origin O to D, and draw a line perpendicular to this segment. Find the intersection of line a and the perpendicular line, mark point A_2, draw a segment from D to A_2, and another segment from A_1 to D_1, find the midpoints E and F of these segments, mark point G on the x-axis, draw a segment from O to A_2, and find the midpoints K of segments O to D and D to A_2.
The prompt above was compiled from the original drawing commands and is for reference only.