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Unit Circle and Trig Graph Relationship

Unit Circle and Trig Graph Relationship
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2018-02-08 05:10
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example dynamically demonstrates the correspondence between points on the unit circle and trigonometric function graphs, revealing the generation principle of trigonometric function images. Core mathematical concepts include the unit circle, trigonometric functions (sine, cosine), angles, and coordinate transformations. GeoGebra commands used in construction include Intersect (intersection), Circle, Rotate, Angle, Line, OrthogonalLine, and Segment. It is suitable for high school mathematics students and teachers to understand the origin and properties of trigonometric function images, as well as for introductory calculus teaching.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A_1
  2. Circle(A_1, 1) → c
  3. Rotate(B, α, A_1) → A
  4. Angle(B, A_1, A) → β
  5. Line(A_1, A) → a
  6. OrthogonalLine(B, xAxis) → b
  7. Intersect(a, b) → C
  8. OrthogonalLine(A, xAxis) → d
  9. Intersect(d, xAxis) → D
  10. Segment(A, D) → e
  11. Segment(D, A_1) → f
  12. Segment(C, B) → g