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Trigonometric Ratios Demo by jordan.ashton

Trigonometric Ratios Demo by jordan.ashton
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2020-02-03 03:23
TrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationships between sine, cosine, and tangent ratios in right triangles. It involves core math concepts like trigonometric definitions, geometric properties of right triangles, and coordinate geometry. Constructed using GeoGebra commands such as Intersect, Segment, OrthogonalLine, Angle, and Circle. Suitable for high school students learning trigonometric principles and geometric interpretations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Segment(A_1, B_1) → r
  3. OrthogonalLine(B_1, xAxis) → g
  4. Intersect(g, xAxis) → C
  5. OrthogonalLine(C, yAxis) → h
  6. Segment(A_1, C) → i
  7. Segment(C, B_1) → j
  8. Angle(B_1, C, A_1) → β
  9. Circle(A_1, B_1) → d
  10. Angle(C, A_1, B_1) → B
  11. Intersect(d, xAxis, 2) → E
  12. Segment(A_1, E) → f
  13. Angle(E, A_1, B_1) → A
  14. Intersect(d, xAxis, 2) → F
  15. Segment(A_1, F) → k

AI Drawing Prompt Reference

Draw a right triangle with its three vertices labeled. From the right angle vertex, draw perpendicular lines to the x-axis and y-axis, forming two smaller right triangles. In one of the smaller triangles, draw a circle centered at the right angle vertex with the hypotenuse as the radius. The circle intersects the x-axis at two points; connect these points to the center and label the angles to demonstrate the relationships between sine, cosine, and tangent ratios.
The prompt above was compiled from the original drawing commands and is for reference only.