Unit Circle and Trigonometric Functions Demonstration

Unit Circle and Trigonometric Functions Demonstration
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2012-11-08 00:08
This example demonstrates the geometric construction of the unit circle and its related trigonometric functions. ①It illustrates concepts such as the unit circle, radius, radians, secant line, sine, cosine, tangent, and shows the ratio relationships of trigonometric functions through angle parameters θ and α. ②Using GeoGebra commands Intersect, Circle, Rotate, Angle, Segment, OrthogonalLine, CircleArc, the construction creates objects like circle A, points B, B', angles θ, α, and text labels text1, enabling dynamic geometric visualization. ③It is suitable for high school trigonometry and university introductory mathematics courses, especially for teaching the properties of the unit circle and trigonometric function graphs.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Intersect(c, xAxis, 2) → B
  4. Rotate(B, θ, A) → B'
  5. Angle(B, A, B') → α
  6. Segment(A, B') → b
  7. OrthogonalLine(B', xAxis) → d
  8. OrthogonalLine(B', xAxis) → a
  9. Intersect(a, xAxis) → C
  10. Segment(A, C) → e
  11. Segment(C, B) → f
  12. Segment(B', C) → g
  13. CircleArc(A, B, B') → k