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Trig Ratios 2: Interactive Right-Triangle Sine, Cosine, and Tangent

Trig Ratios 2: Interactive Right-Triangle Sine, Cosine, and Tangent
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2019-04-23 16:20
TriangleAngleTrigonometryGeometric ConstructionSlider Animation
This GeoGebra example provides an interactive visualization of trigonometric ratios (sine, cosine, tangent) in a right triangle, showing how these ratios change as the acute angle varies. Core mathematical concepts include right-triangle trigonometry, side-angle relationships, and the dynamic behavior of trigonometric functions. The construction uses commands such as Segment, Ray, Circle, Rotate, Angle, OrthogonalLine, and Textfield to build a right triangle with a movable angle α, displaying real-time numeric values. Key objects include points A, B, C, segments a, b, c, angle α, and multiple auxiliary points and text labels. Suitable for middle-to-high school students learning basic trigonometry, and for teachers demonstrating the transition from geometric ratios to functional values.

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 a movable acute angle α. Construct the three sides of the triangle using rotation and intersection, and create related lines and points based on angle α. Display the degree of angle α and dynamically adjust the lengths of the sides and the degree of angle β when changing angle α. Use a slider to control the size of angle α and build each part of the triangle through rotation and intersection operations.
The prompt above was compiled from the original drawing commands and is for reference only.