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Trigonometric Ratios and Geometric Construction

Trigonometric Ratios and Geometric Construction
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2016-02-03 10:33
TriangleAngleTrigonometryGeometric ConstructionSlider Animation
① This GeoGebra example dynamically demonstrates the relationships between trigonometric ratios (sine, cosine, tangent) and the sides and angles of right triangles, using rotations and rays to show how ratios change with angle. ② Core mathematical concepts include definitions of trigonometric functions, similar triangles, angle measure in degrees/radians, and trigonometric lines in the unit circle. ③ Construction details: from the summary, commands such as Segment, OrthogonalLine, Point, Polygon, Angle, Rotate, Ray, and Intersect are used to create multiple triangles (poly1, poly2) and auxiliary lines (perpendiculars, rotated sides), with angles α, β, γ controlling the dynamic figure. ④ Suitable for high school students learning trigonometric definitions, identities, or geometry-algebra connections, and for teachers creating interactive lessons or for pre-calculus review.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_2
  2. OrthogonalLine(A, a_2) → b_2
  3. Point(b_2) → C
  4. Polygon(B, A, C) → poly1, c, b, a
  5. Angle(B, A, C) → α
  6. Angle(A, C, B) → β
  7. Angle(C, B, A) → γ
  8. Segment(A', B') → d
  9. OrthogonalLine(A', d) → e
  10. Point(e) → G
  11. Rotate(A', (-γ), B') → D'
  12. Angle(D', B', A') → δ
  13. Ray(B', D') → f
  14. Intersect(e, f) → C'
  15. Polygon(A', B', C') → poly2, c', a', b'
  16. Angle(A', C', B') → ε
  17. Angle(B', A', C') → ζ