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Trigonometric Ratios by Philip K

Trigonometric Ratios by Philip K
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2016-03-11 01:44
AngleTrigonometryGeometric Construction
This example demonstrates the concept of trigonometric ratios. By constructing the sides and angles of a triangle, it illustrates the definitions of sine, cosine, and tangent. GeoGebra commands such as Segment, Dilate, and Angle are used for geometric transformations and angle measurement. Suitable for students in middle school and above to learn the basic properties and applications of trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. OrthogonalLine(A, a) → b
  3. Point(b) → C
  4. Segment(C, B) → c
  5. Segment(C, A) → d
  6. Dilate(A, scale, D) → A'
  7. Dilate(B, scale, D) → B'
  8. Segment(A', B') → a'
  9. Dilate(C, scale, D) → C'
  10. Dilate(B, scale, D) → B'_1
  11. Segment(C', B'_1) → c'
  12. Dilate(C, scale, D) → C'_1
  13. Dilate(A, scale, D) → A'_1
  14. Segment(C'_1, A'_1) → d'
  15. Angle(A, C, B) → α
  16. Angle(C, B, A) → β
  17. Angle(A', C', B') → γ
  18. Angle(C', B', A') → δ
  19. Angle(B, A, C) → ε
  20. Angle(B', A', C') → ζ

AI Drawing Prompt Reference

Draw a triangle ABC with points A, B, and C as vertices. First, draw side AB, then draw a perpendicular line to AB through A, intersecting at C, and then draw sides BC and AC. Next, use point D as the center of dilation and dilate points A, B, and C with different scales to get A', B', and C'. Then, draw sides A'B', B'C', and C'A'. Finally, measure angles α, β, γ, δ, ε, and ζ, which represent the interior angles of triangles ABC and A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.