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Unit Circle and Sine Cosine Functions

Unit Circle and Sine Cosine Functions
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2019-10-09 22:08
CircleFunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically demonstrates the correspondence between a point on the unit circle and the sine and cosine function graphs in the Cartesian coordinate system, intuitively showing the definition of trigonometric functions. Core mathematical concepts include the unit circle, trigonometric functions (sine, cosine), Cartesian coordinates, and the conversion between angles and coordinates. Construction highlights involve GeoGebra commands/objects like Circle, Point, CircleArc, OrthogonalLine, Intersect, Segment, Polygon, and Angle. Suitable for high school mathematics students learning the basic properties of trigonometric functions and university foundational mathematics teaching.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. CircleArc(A, B, C) → d
  4. OrthogonalLine(C, xAxis) → a
  5. OrthogonalLine(C, yAxis) → b
  6. Intersect(b, yAxis) → D
  7. Segment(C, D) → e
  8. Intersect(a, xAxis) → E
  9. Segment(C, E) → f
  10. OrthogonalLine(Y, xAxis) → g
  11. Intersect(g, xAxis) → F
  12. Segment(Y, F) → h
  13. Segment(X, F) → i
  14. Segment(A, F) → n
  15. Polygon(G, G2, G3) → poly1, g3, g_1, g2
  16. Angle(G2, G, G3) → α

AI Drawing Prompt Reference

Draw a unit circle with a point on it, showing the correspondence between this point and the sine and cosine function graphs in the Cartesian coordinate system. Create two perpendicular lines to the x-axis and y-axis, intersecting them at two points. Connect these points to the point on the circle with line segments. Also, draw an angle to intuitively demonstrate the definition of trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.