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The 3 Main Trigonometric Ratios by Tim Brzezinski

The 3 Main Trigonometric Ratios by Tim Brzezinski
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2015-08-22 10:38
TriangleAngleFunctionTrigonometry
In collections GA Chapter 8: Right Triangles and Trigonometry
This example demonstrates the basic trigonometric ratios in a right triangle, focusing on sine, cosine, and tangent. The key mathematical concepts involve understanding these ratios through geometric construction. The construction uses GeoGebra commands such as Segment, OrthogonalLine, Angle, and Vector to create the triangle and related elements. It is suitable for middle or high school mathematics education to help students grasp the fundamental properties and graphs of trigonometric functions.

GeoGebra Commands & Parameters

  1. Segment(A, C) → adjacent
  2. OrthogonalLine(C, adjacent) → b_2
  3. Point(b_2) → B
  4. Segment(A, B) → hypotenuse
  5. Segment(B, C) → opposite
  6. Angle(B, C, A) → α
  7. Vector(D, E) → u
  8. Vector(F, G) → v
  9. Translate(A, v) → A'_3
  10. Translate(C, v) → B'_3
  11. Translate(B, v) → C'_3
  12. Translate(A, v) → A'_1
  13. Translate(C, v) → B'_1
  14. Translate(A, v) → A'_2
  15. Translate(B, v) → C'_1
  16. Translate(B, v) → C'_2
  17. Translate(C, v) → B'_2
  18. Translate(D, v) → D'
  19. Dilate(C'_1, 0.5, H) → L
  20. Dilate(C'_2, 0.5, H) → M
  21. Angle(C, A, B) → β
  22. Segment(C, B) → c
  23. Midpoint(hypotenuse) → I
  24. Midpoint(opposite) → J
  25. Midpoint(adjacent) → K
  26. Point(d) → P
  27. Vector(P, J) → w
  28. Vector(P, I) → m
  29. Vector(P, K) → n
  30. Vector(N, O) → p
  31. Segment(A, B) → q
  32. Segment(B, C) → r
  33. Segment(C, A) → s

AI Drawing Prompt Reference

Draw a right triangle with its three sides labeled as adjacent, opposite, and hypotenuse. Mark one angle inside the triangle and label its measure. From the midpoint of the hypotenuse and the opposite side, draw perpendicular lines to the adjacent side, marking the feet of the perpendiculars. Then, translate the triangle along the perpendicular bisector of the opposite side to create three new triangles and observe their relationships with the original triangle.
The prompt above was compiled from the original drawing commands and is for reference only.