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The 3 Main Trigonometric Ratios

The 3 Main Trigonometric Ratios
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2019-11-10 00:28
AngleVectorTrigonometryGeometric Construction
This example demonstrates the three main trigonometric ratios: sine, cosine, and tangent. It involves core mathematical concepts such as the basic definitions and properties of trigonometric functions. Using GeoGebra commands like Segment, OrthogonalLine, Point, etc., a dynamic triangle is constructed to show how these ratios change with the angle. Suitable for students at the junior high school level and above to learn the basic concepts 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 labeled hypotenuse, adjacent side, and opposite side, and display one acute angle. Then, using vector translations from the right angle vertex, construct three congruent triangles to show the change in trigonometric ratios. Mark the midpoints of each side, draw vectors from the right angle to these midpoints, and finally connect all vertices to complete the figure.
The prompt above was compiled from the original drawing commands and is for reference only.