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Tracing the Sine Graph

Tracing the Sine Graph
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2015-05-19 09:53
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the sine function's graph and its geometric construction. Key mathematical concepts include trigonometry, geometric construction, and coordinate geometry. The construction involves GeoGebra commands such as Intersect, Circle, Point, etc. It is suitable for high school students or math enthusiasts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1.0) → c
  3. Point(c) → P
  4. OrthogonalLine(P, yAxis) → a
  5. Intersect(a, yAxis) → B
  6. Segment(P, B) → b
  7. OrthogonalLine(P, xAxis) → d
  8. Intersect(d, xAxis) → C
  9. Segment(P, C) → e
  10. Segment(A, P) → f
  11. Angle(xAxis, f) → θ
  12. Vector(M, N) → u
  13. Vector(O, Q) → v
  14. Point(u) → D
  15. Point(u) → E
  16. Point(Circle[D, 4.3]) → F
  17. Segment(D, F) → i
  18. Point(Circle[E, 4.3]) → G
  19. Segment(E, G) → j
  20. Point(i) → H
  21. Point(j) → I
  22. Point(i) → J
  23. Point(j) → K
  24. Point(i) → L
  25. Point(j) → R
  26. Point(i) → S
  27. Point(j) → T
  28. Segment(H, I) → k
  29. Segment(J, K) → l
  30. Segment(L, R) → m
  31. Segment(S, T) → n

AI Drawing Prompt Reference

Draw the graph of a sine function, showing its geometric construction. Start by plotting the coordinate axes and finding their intersection point. Draw a unit circle centered at this point, and connect the point on the circle to the axes with perpendicular lines. Form segments by connecting the intersection points. Then, draw a line parallel to the x-axis from the point on the circle, and connect the intersection points to form another segment. Finally, draw a large circle centered at the point on the circle, and connect multiple points on the large circle to form a wavy curve representing the sine function.
The prompt above was compiled from the original drawing commands and is for reference only.