Cosine Wave Demonstration

Cosine Wave Demonstration
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2016-10-31 02:39
This example demonstrates the formation of a cosine wave and its relationship with the unit circle. It involves core mathematical concepts such as trigonometric functions, unit circle, orthocenter, standard deviation, parametric curves, volume, and subtraction. The construction highlights the use of GeoGebra commands and objects like segments, points, intersections, circles, orthogonal lines, and angles. Suitable for high school and above, it illustrates the connection between trigonometric function graphs and parametric equations, as well as the application of geometric constructions in function studies.

GeoGebra Commands & Parameters

  1. Segment((0, 0), (360, 0)) → a
  2. Point(a) → A
  3. Intersect(xAxis, yAxis) → B
  4. Point(xAxis) → C
  5. Circle(B, C) → c
  6. Point(c) → D
  7. OrthogonalLine(D, xAxis) → d
  8. Intersect(d, xAxis) → F
  9. Segment(D, F) → e
  10. Intersect(xAxis, yAxis) → G
  11. Segment(G, D) → f
  12. Segment(F, G) → g
  13. Angle(xAxis, f) → α
  14. Segment((0, 0), (360, 0)) → h