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Trigonometric Ratios Demo by PCARTS

Trigonometric Ratios Demo by PCARTS
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2016-11-17 18:19
AngleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the calculation and visualization of trigonometric ratios by constructing a right triangle and measuring the relationships between side lengths and angles. Core math concepts include trigonometric functions (sine, cosine, tangent), properties of right triangles, distance and angle measurements. GeoGebra commands and objects used in construction are Ray, Point, OrthogonalLine, Intersect, Angle, Distance, Segment. Suitable for high school mathematics teaching to help students intuitively understand the definitions and applications of trigonometric functions.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Ray(A, C) → g
  3. Point(f) → D
  4. OrthogonalLine(D, f) → h
  5. Intersect(h, g) → E
  6. Intersect(g, h) → F
  7. Angle(f, g) → α
  8. Distance(A, D) → distanceAD
  9. Distance(E, D) → distanceED
  10. Distance(A, E) → distanceAE
  11. Distance(A, E) → AE
  12. Distance(A, D) → AD
  13. Distance(E, D) → ED
  14. Angle(A, D, E) → β
  15. Segment(A, D) → i
  16. Segment(A, E) → j
  17. Segment(D, E) → k

AI Drawing Prompt Reference

Draw a right triangle with point A as the right angle, and points B and C as the other two vertices. Construct a perpendicular line from point D to line f, intersecting line g at point E. Measure angle α and the lengths of segments AD, AE, and ED.
The prompt above was compiled from the original drawing commands and is for reference only.