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Trigonometric Ratios Demo by evazus

Trigonometric Ratios Demo by evazus
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2012-05-16 22:24
TrigonometryCoordinate GeometryGeometric Construction
In collections Trig Ratios
This example demonstrates how to determine trigonometric ratios by comparing the ratios of opposite to hypotenuse and adjacent to hypotenuse. The key mathematical concepts involved include sine, cosine, and tangent ratios. Construction involves using GeoGebra commands such as Line, OrthogonalLine, Point, and Polygon to create triangles and related graphs. Suitable for middle or high school mathematics teaching to understand the basic properties and construction of trigonometric functions.

GeoGebra Commands & Parameters

  1. Line(A, C) → a
  2. OrthogonalLine(C, a) → b
  3. Point(b) → B
  4. Polygon(A, C, B) → poly1, c, a_1, b_1
  5. Point(b_1) → D
  6. Line(D, a_1) → d
  7. Intersect(d, c) → E
  8. Segment(E, D) → e
  9. Distance(A, E) → distanceAE
  10. Distance(A, C) → distanceAC
  11. Distance(E, D) → distanceED
  12. Distance(C, B) → distanceCB
  13. Angle(B, C, A) → α
  14. Angle(D, E, A) → β
  15. Distance(A, D) → distanceAD
  16. Distance(A, B) → distanceAB
  17. Angle(E, A, D) → γ
  18. Angle(A, D, E) → δ
  19. Angle(A, B, C) → ε

AI Drawing Prompt Reference

Draw a right triangle ABC with point A at the origin, point C on the x-axis, and point B on the y-axis. Construct the altitude and perpendicular lines to find points D and E, then connect these points to form a new triangle. Measure the lengths of the sides and angles, and calculate the trigonometric ratios.
The prompt above was compiled from the original drawing commands and is for reference only.