Unit Circle with Sine Graph

Unit Circle with Sine Graph
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2016-10-14 04:43
① This example dynamically links a point rotating on the unit circle to the corresponding sine function graph, visually demonstrating the geometric relationship between an angle and its sine value. ② Core mathematical concepts include the unit circle, sine function, angle and radian conversion, periodicity of trigonometric functions, and function graphing. ③ Construction highlights: using GeoGebra commands such as Intersect, Point, Circle, Rotate, Angle, Segment, OrthogonalLine, and Polygon to build the unit circle, the rotating angle θ, the sine segment, and the corresponding graph point, with a slider or animation to update the angle in real time. ④ Suitable for high school trigonometry lessons, college pre-calculus review, and interactive exploration for math enthusiasts.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Circle(A, B) → c_1
  4. Rotate(B, θ, A) → B'
  5. Angle(B, A, B') → α
  6. Segment(A, B') → d
  7. OrthogonalLine(B', xAxis) → h
  8. Intersect(h, xAxis) → D
  9. Segment(A, B) → a
  10. Segment(A, B) → c
  11. Segment(B', D) → e
  12. Intersect(c_1, xAxis, 2) → E
  13. Segment(E, D) → g
  14. Polygon(D, B', A) → poly1, a_1, d_1, b'