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Interactive Unit Circle

Interactive Unit Circle
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2019-02-07 03:19
CircleTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates the relationship between the unit circle and trigonometric functions through dynamic interaction, showing the geometric meaning of angles, sine values, and cosine values. Core mathematical concepts include the unit circle, trigonometric functions (sine, cosine), angles, coordinates, and geometric construction. It utilizes GeoGebra commands and objects such as Intersect, Circle, Point, Segment, Angle, OrthogonalLine, Line, and LaTeX. Suitable for high school students learning about the definition of trigonometric functions and the application of the unit circle.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → I
  4. Segment(I, A) → g
  5. Angle(E, A, I) → α
  6. OrthogonalLine(I, xAxis) → h
  7. Intersect(h, xAxis) → Q
  8. Line(A, Q) → i
  9. Segment(I, Q) → j
  10. Segment(A, Q) → k
  11. LaTeX(Tangent, true, true) → text1
  12. LaTeX(Sine, true, true) → text2
  13. LaTeX(Cosine, true, true) → text3