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Explore Trigonometric Ratios

Explore Trigonometric Ratios
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2016-03-09 20:52
TriangleAngleTrigonometryGeometric Construction
This example demonstrates the geometric meaning of trigonometric ratios (sine, cosine) in right triangles. It involves core concepts like the definition of trigonometric functions, similar triangles, and relationships between side lengths. Construction highlights include using Rotate, Angle, Ray, Point, OrthogonalLine, Intersect, and Segment commands to build triangles and auxiliary lines, with labeled key points and edges. Suitable for high school students to understand the definition and practical application of trigonometric functions.

GeoGebra Commands & Parameters

  1. Rotate(A, α, B) → A'
  2. Angle(A, B, A') → β
  3. Ray(B, A) → a
  4. Ray(B, A') → b
  5. Point(a) → C
  6. OrthogonalLine(C, a) → c
  7. Intersect(c, b) → D
  8. Angle(D, C, B) → γ
  9. Segment(D, C) → d
  10. Segment(B, C) → e
  11. Segment(B, D) → f
  12. Segment(B, D) → j
  13. Segment(D, C) → k
  14. Segment(C, B) → l