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Cosine Function: Special Property

Cosine Function: Special Property
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2016-11-29 23:56
FunctionTrigonometryTransformation
In collections Trigonometric Identities
This example dynamically illustrates the special property of the cosine function, involving trigonometric identities. Using GeoGebra commands such as mirror, rotate, and translate, the nature of the cosine function is vividly demonstrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Mirror(g, x = 0) → g_1
  2. Point(g) → F
  3. Intersect(h, y = 0) → G
  4. Mirror(G, x = 0) → G'
  5. Mirror(F, x = 0) → F'
  6. Dilate(H, If[0 < e ≤ 1, 1 - e, 0], G) → H'
  7. Segment(H, H') → i
  8. Dilate(G, If[1 < e ≤ 2, 2 - e, 0], F) → G'_1
  9. Segment(G, G'_1) → j
  10. Rotate(H, If[2 < e ≤ 3, ((-(e - 2)) * π), (-π)], H) → H'_1
  11. Rotate(H', If[2 < e ≤ 3, ((-(e - 2)) * π), (-π)], H) → H''
  12. Segment(H'_1, H'') → i'
  13. Dilate(G', If[3 < e ≤ 4, 4 - e, 0], F') → G''
  14. Segment(G', G'') → k
  15. Dilate(F, If[4 < e ≤ 5, 5 - e, 0], F') → F'_1
  16. Vector(F, F'_1) → u
  17. Translate(G, u) → G'_2
  18. Translate(G'_1, u) → I
  19. Segment(G'_2, I) → j'