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Unit Circle and Trig Graphs

Unit Circle and Trig Graphs
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2017-06-16 04:32
CircleFunctionTrigonometryGeometric ConstructionGraphing
This example demonstrates the relationship between the unit circle and trigonometric graphs (sine and cosine functions). It involves core mathematical concepts such as the definition of the unit circle, trigonometric function definitions, angle and radian conversion, periodicity, etc. The construction uses GeoGebra commands and objects like Intersect (intersection), Rotate (rotation), Angle (angle), Segment (segment), Midpoint (midpoint), and Tangent (tangent). It is suitable for high school mathematics teaching to help students visually understand the origin and properties of trigonometric graphs.

GeoGebra Commands & Parameters

  1. Intersect(circle, xAxis, 2) → A
  2. Intersect(xAxis, yAxis) → B
  3. Rotate(A, θ°, B) → P
  4. Angle(A, B, P) → α
  5. Angle(P, B, A) → β
  6. Rotate(A, 359.9°, B) → A'
  7. Angle(A, B, A') → γ
  8. Rotate(A, 359.9°, B) → A'_1
  9. Rotate(A, 359.9°, B) → A'_2
  10. Angle(A, B, A'_2) → δ
  11. Rotate(A, 359.9°, B) → A'_3
  12. Angle(A, B, A'_3) → ε
  13. Segment((x(P), 0), P) → a
  14. Segment(B, P) → b
  15. Segment((θ, 0), (θ, y(P))) → d
  16. Midpoint(C, P) → D
  17. Midpoint(E, F) → G
  18. Segment(B, C) → e
  19. Midpoint(B, C) → H
  20. Segment(E, I) → h
  21. Midpoint(E, I) → J
  22. Tangent(P, circle) → k,
  23. Intersect(k, xAxis) → K
  24. Segment(P, K) → l
  25. Midpoint(K, P) → L
  26. Segment(E, M) → m
  27. Midpoint(M, E) → N