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Trigonometric Ratios and Unit Circle Demo

Trigonometric Ratios and Unit Circle Demo
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2017-04-20 00:50
CircleVectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between trigonometric functions and the unit circle interactively, visually showing the geometric meanings of sine, cosine, tangent, etc. Core math concepts include trigonometric function definitions, unit circle, trigonometric ratios, coordinate system, vectors, etc. It uses GeoGebra commands/objects like Intersect, Circle, OrthogonalLine, Segment, Ray, Point, Vector, Angle. Suitable for high school mathematics teaching to help students understand the geometric basis of trigonometric functions and enhance spatial imagination.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, r) → c
  3. OrthogonalLine(D, xAxis) → f
  4. Intersect(f, xAxis) → B
  5. Segment(A, B) → g
  6. Segment(B, D) → h
  7. Segment(D, A) → i
  8. Ray(A, D) → s
  9. Point(s) → C
  10. Vector(A, C) → u
  11. Point(xAxis) → E
  12. Ray(A, E) → t
  13. Intersect(c, xAxis, 2) → F
  14. Angle(F, A, D) → α
  15. Vector(A, F + (0.5, 0)) → v
  16. Point(f) → G
  17. Angle(G, B, A) → β

AI Drawing Prompt Reference

Draw a unit circle in a coordinate system with axes. Mark the origin and the intersection points with the axes. Draw a ray from the origin to a point on the circle and label it. Take another point on the ray and connect it to the origin to form a vector. Also, draw a ray from the origin along the positive x-axis and mark its intersection with the circle. Finally, draw a line segment from the intersection point to the center of the circle and a perpendicular line from the intersection point to the left and upward, labeling the relevant angles and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.