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Trigonometric Ratios by Axel Ambert Morales

Trigonometric Ratios by Axel Ambert Morales
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2018-10-01 22:56
AngleTrigonometryGeometric Construction
This example demonstrates the relationships of trigonometric ratios. It involves core concepts such as sine, cosine, and tangent. Using GeoGebra commands like Segment, Angle, and Circle, it constructs the relationships between angles and sides in a triangle. Suitable for students at the middle school level and above to learn the basic properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. OrthogonalLine(B, f) → g
  3. Rotate(B, (a * π / 180), A) → B'
  4. Angle(B, A, B') → α
  5. Ray(A, B') → h
  6. Circle(B, 2) → c
  7. Intersect(c, g, 2) → C
  8. Ray(B, C) → i
  9. Intersect(h, i) → D
  10. Segment(B, D) → j
  11. Segment(A, D) → k
  12. Polygon(A, B, D) → poly1, d, a_1, b
  13. Rotate(B, If[0 < e ≤ 1, (-((e * (π / 2 - α)))), α - π / 2], D) → B'_1
  14. Rotate(D, If[0 < e ≤ 1, (-((e * (π / 2 - α)))), α - π / 2], D) → D'
  15. Segment(B'_1, D') → j'
  16. Rotate(A, If[0 < l ≤ 1, (α * l), α], A) → A'
  17. Rotate(B, If[0 < l ≤ 1, (α * l), α], A) → B'_2
  18. Segment(A', B'_2) → f'
  19. Rotate(B, If[0 < m ≤ 1, (m * π / 2), π / 2], B) → B'_3
  20. Rotate(D, If[0 < m ≤ 1, (m * π / 2), π / 2], B) → D'_1
  21. Segment(B'_3, D'_1) → j'_1
  22. Textfield(a) → InputBox1
  23. Angle(D, B, A) → β

AI Drawing Prompt Reference

Draw a right triangle with one acute angle. From the vertex of this angle, draw a perpendicular line to the hypotenuse, meeting it at a point. With the vertex as the center and the hypotenuse as the diameter, draw a circle. Let it intersect the perpendicular line at another point. Connect this point to the vertex to form a new triangle. Label the lengths of the sides and the measures of the angles to illustrate trigonometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.