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Trigonometric Ratios in Right Triangles by skapralos

Trigonometric Ratios in Right Triangles by skapralos
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2017-01-27 02:08
TriangleTrigonometryGeometric Construction
This example dynamically demonstrates how trigonometric ratios (sine, cosine, tangent) change as the angle and triangle size vary in a right triangle. It involves core concepts like trigonometry, right triangle properties, and geometric constructions. The construction uses GeoGebra commands such as Point, Intersect, Rotate, Angle, Ray, OrthogonalLine, and Segment. Suitable for high school mathematics education to visually understand the definitions and dynamic behavior of trigonometric functions.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → O
  3. Rotate(A, θ, O) → C
  4. Angle(A, O, C) → β
  5. Ray(O, C) → a
  6. Point(a) → B
  7. OrthogonalLine(B, xAxis) → b
  8. Intersect(b, xAxis) → D
  9. Segment(B, D) → c
  10. Segment(O, D) → d
  11. Segment(O, B) → e

AI Drawing Prompt Reference

Draw a right triangle with point A on the x-axis, point O at the intersection of the x-axis and y-axis, point C obtained by rotating point A around point O, angle β formed by points A, O, and C, line a as the ray through points O and C, point B on line a, line b as the perpendicular line to the x-axis through point B, point D as the intersection of line b and the x-axis, line segment c connecting points B and D, line segment d connecting points O and D, and line segment e connecting points O and B.
The prompt above was compiled from the original drawing commands and is for reference only.