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Cotangent Function Exploration

Cotangent Function Exploration
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2018-10-25 21:06
FunctionTrigonometryCoordinate GeometryGeometric ConstructionGraphing
This example demonstrates the cotangent function graph and its intuitive relationship with the unit circle and special triangles. Key math concepts include cotangent definition, unit circle, vectors, symmetry, and coordinate geometry. Construction involves commands like Angle, Ray, Segment, Intersect, Vector, Mirror, OrthogonalLine, Dilate, Translate, Rotate, Circle. Suitable for high school students to understand trigonometric properties and geometric meanings.

GeoGebra Commands & Parameters

  1. Angle(C, B, A) → α
  2. Ray(B, A) → i
  3. Segment(B, C) → k
  4. Intersect(i, j) → D
  5. Angle(D, C, B) → β
  6. Vector(C, D) → u
  7. Mirror(C, B) → C'
  8. OrthogonalLine(C', xAxis) → l
  9. Intersect(l, i) → E
  10. Vector(C', E) → v
  11. Angle(D, B, C) → θ
  12. Dilate(D, If[0 < a ≤ 1, 1 - a, 0], F) → D'
  13. Vector(D, D') → b
  14. Translate(C, b) → C'_1
  15. Vector(C'_1, D') → d
  16. Intersect(c, m) → G, H
  17. OrthogonalLine(G, m) → n
  18. OrthogonalLine(H, m) → q
  19. Segment(B, G) → r
  20. Segment(B, H) → s
  21. Intersect(n, i) → I
  22. Segment(G, I) → t
  23. Angle(G, I, B) → γ
  24. Vector(G, I) → e
  25. Angle(B, G, I) → δ
  26. Dilate(G, If[0 < a ≤ 1, 1 - a, 0], K) → G'
  27. Vector(G, G') → u_1
  28. Translate(I, u_1) → I'
  29. Rotate(I', If[0 < a ≤ 1, (a * π / 2), π / 2], G') → I''
  30. Vector(G', I'') → v_1
  31. Ray(G, I) → h_1
  32. Circle(I, 1) → c_1
  33. Ray(I, L) → i_1
  34. Angle(L, I, B) → ε