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Trigonometric Ratios and Circles

Trigonometric Ratios and Circles
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2018-10-14 16:57
CircleFunctionTrigonometryGeometric Construction
This example demonstrates the relationship between trigonometric ratios and circles, involving concepts like trigonometry, circles, and graphing. The construction uses GeoGebra commands such as Circle, Point, Segment, Line, and Tangent to illustrate periodic and symmetric properties of trigonometric functions. Suitable for high school students or college students learning about trigonometric applications in geometry and coordinate systems.

GeoGebra Commands & Parameters

  1. Circle((0, 0), 1) → c
  2. Point(c) → A
  3. Segment((0, 0), A) → a
  4. Line((0, 0), (1, 0)) → b
  5. Line((0, 0), (0, 1)) → d
  6. Tangent(A, c) → e,
  7. Intersect(d, e) → B
  8. Intersect(b, e) → C
  9. OrthogonalLine(A, b) → f
  10. OrthogonalLine(A, d) → g
  11. Intersect(d, g) → D
  12. Intersect(b, f) → E
  13. Intersect(c, d, 2) → F
  14. Intersect(c, b, 2) → G
  15. Angle(b, a) → θ
  16. Segment(A, E) → h
  17. Intersect(b, d) → H
  18. Segment(D, H) → i
  19. Segment(A, D) → j
  20. Segment(E, H) → k
  21. Translate(C, (0, -0.3)) → C'
  22. Translate(H, (0, -0.3)) → H'
  23. Segment(H', C') → l
  24. Segment(H, H') → m
  25. Segment(C, C') → n
  26. Translate(H, (-0.3, 0)) → H'_1
  27. Translate(B, (-0.3, 0)) → B'
  28. Segment(B', H'_1) → p
  29. Segment(B, B') → q
  30. Segment(H, H'_1) → r
  31. Segment(E, G) → s
  32. Segment(G, C) → t
  33. Segment(A, C) → a_1
  34. Segment(A, B) → b_1
  35. Segment(B, F) → c_1
  36. Segment(F, D) → d_1

AI Drawing Prompt Reference

Draw a unit circle centered at the origin with a radius of 1. Take a point A on the circle and draw a line segment a from the origin to A. Draw the x-axis and y-axis, and let them intersect the tangent line e at points B and C. Draw perpendicular lines to the x-axis and y-axis, and let them intersect the tangent line e at points D and E. Draw a line segment from A to E, which intersects the x-axis and y-axis at points H and C'. Translate C' down by 0.3 units to get C', and draw a line segment from C' to H, and from C to C'. Translate H left by 0.3 units to get H', and draw a line segment from H' to B, and from B to H'. Draw a line segment from B to E, from E to G, from G to C, from A to C, from A to B, from B to F, and from F to D.
The prompt above was compiled from the original drawing commands and is for reference only.