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Trigonometric Ratios Demo by frikkie81 (2)

Trigonometric Ratios Demo by frikkie81 (2)
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2019-04-23 16:13
AngleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationships between side lengths and angles in right triangles through trigonometric ratios (sine, cosine, tangent). It involves core math concepts like right triangles, angle measurement, and trigonometric functions. The construction uses GeoGebra commands such as Segment, OrthogonalLine, Rotate, Angle, Circle, Intersect, Polygon, and Textfield to visualize and calculate these ratios. Suitable for high school students learning trigonometry and its applications in geometry and function graphing.

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, labeling the opposite and adjacent sides. Visualize the sine, cosine, and tangent ratios using a circle and line segments. Start by drawing a right triangle with one leg and the hypotenuse. Then draw a perpendicular line from the right angle to the hypotenuse. Draw a circle with the right angle as the center and the hypotenuse as the diameter, intersecting the perpendicular line at two points. Connect these points to the right angle to form three smaller triangles. Measure and label the angles of these triangles, and represent the sine, cosine, and tangent ratios accordingly.
The prompt above was compiled from the original drawing commands and is for reference only.