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Trigonometric Ratios Demo by chisunch1

Trigonometric Ratios Demo by chisunch1
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2015-09-05 17:06
AngleTrigonometryGeometric Construction
This example dynamically demonstrates the relationships between sides and angles in a right triangle, visually showcasing the definitions of sine, cosine, and tangent ratios. It involves core math concepts like trigonometric functions, right triangles, side length proportions, and angle measurement. GeoGebra commands and objects such as Line, OrthogonalLine, Point, Segment, Angle, Midpoint, and Vector are used to construct the triangle and auxiliary lines precisely. Suitable for high school mathematics teaching to help students understand trigonometric ratio calculations and geometric significance.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(A, B) → AB
  5. Segment(C, B) → BC
  6. Segment(A, C) → AC
  7. Angle(C, B, A) → ABC
  8. Angle(C, A, B) → α
  9. Angle(A, C, B) → β
  10. Midpoint(A, B) → D
  11. Midpoint(B, C) → E
  12. Midpoint(C, A) → F
  13. Segment(A, E) → e
  14. Segment(C, D) → f
  15. Point(f) → G
  16. Point(f) → H
  17. Point(e) → I
  18. Point(e) → J
  19. Vector(J, I) → u
  20. Vector(H, G) → v
  21. Segment(K, L) → c
  22. Segment(M, N) → d
  23. Segment(O, P) → g
  24. Segment(Q, R) → h
  25. Segment(S, T) → i
  26. Segment(U, V) → j

AI Drawing Prompt Reference

Draw a right triangle with the right angle at the right end of a horizontal base, the vertical leg rising from that point; label the three interior angles to illustrate the definitions of sine, cosine, and tangent; mark the midpoints of all three sides, draw the medians from each vertex to the opposite midpoint, and place auxiliary points on those medians to show the side‑length ratios.
The prompt above was compiled from the original drawing commands and is for reference only.