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Trigonometry and Unit Circle by Michael Gillespie

Trigonometry and Unit Circle by Michael Gillespie
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2016-02-15 04:27
CircleVectorFunctionTrigonometryCoordinate Geometry
This example demonstrates the relationship between trigonometric functions and the unit circle interactively, visually showing the combination of geometric and algebraic concepts such as angles, coordinates, and vectors. Core mathematical concepts include the definition of trigonometric functions, the unit circle, angle measurement, vector representation, and analytical geometry. Key GeoGebra commands used in construction include Intersect, Circle, Rotate, Angle, Segment, OrthogonalLine, and Slope. Suitable for high school mathematics teaching to help students understand the geometric meaning of trigonometric functions and their application in coordinate systems.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, Angle, A) → B'
  5. Angle(B, A, B') → α
  6. Segment(A, B') → a
  7. OrthogonalLine(B', xAxis) → b
  8. Intersect(b, xAxis) → C
  9. Segment(C, B') → d
  10. Segment(A, C) → f
  11. Angle(B', C, A) → β
  12. Slope(a) → m