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Unit Circle and Sine & Cosine Graphs

Unit Circle and Sine & Cosine Graphs
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2020-02-18 21:01
CircleTrigonometryCoordinate Geometry
This example demonstrates the relationship between the unit circle and the graphs of sine and cosine functions. Key mathematical concepts include trigonometry, unit circle, and coordinate geometry. Using GeoGebra commands such as Segment, Intersect, Circle, etc., it dynamically shows the correspondence between angles and sine/cosine values. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Segment((-1, sin(Θ)), (1, sin(Θ))) → segSin
  2. Segment((cos(Θ), -1), (cos(Θ), 1)) → segCos
  3. Intersect(segSin, segCos) → Pr
  4. Circle((0, 0), 1) → uc
  5. Vector((1.5 + Θ / 2, 0), (1.5 + Θ / 2, sin(Θ))) → vecSin
  6. Vector((1, 0), (1, sin(Θ))) → vecSin2
  7. Vector((0, 1), (cos(Θ), 1)) → vecCos2
  8. Vector((1.5 + Θ / 2, 0), (1.5 + Θ / 2, cos(Θ))) → vecCos
  9. Segment((1.3, 0), (4.841592653589793, 0)) → xa
  10. Segment((-1.1, 0), (1.1, 0)) → cx
  11. Segment((0, -1.1), (0, 1.1)) → cy
  12. Line((Θ / 2 + 1.5, 0), (Θ / 2 + 1.5, 1)) → e
  13. Segment((0, 0), (cos(Θ), sin(Θ))) → segRadius
  14. Segment((cos(Θ), 1), (1.5 + Θ / 2, 1)) → segCosCon1
  15. Segment((1.5 + Θ / 2, 1), (1.5 + Θ / 2, cos(Θ))) → segCosCon2
  16. Segment((1, sin(Θ)), (1.5 + Θ / 2, sin(Θ))) → segSinCon
  17. Angle(cx, segRadius) → α