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Special Property of Cosine and Secant Functions

Special Property of Cosine and Secant Functions
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2016-11-29 10:07
CircleAngleFunctionTrigonometryGeometric Construction
In collections Trigonometric Identities
This example dynamically demonstrates the geometric relationship and special properties of cosine and secant functions. Key math concepts include trigonometric functions, circles, similar triangles, and geometric transformations. Construction highlights involve GeoGebra commands like CircleArc, Point, Circle, Intersect, Ray, CircleSector, Mirror, Angle, Dilate, Segment, Rotate, and Polygon. Suitable for high school and above mathematics learners to understand the geometric meaning and properties of trigonometric functions.

GeoGebra Commands & Parameters

  1. CircleArc(B, A, J) → f_1
  2. CircleArc(B, A, I) → p
  3. Point(p) → C
  4. Circle(B, A) → c
  5. Intersect(f, h) → D
  6. Ray(B, C) → i
  7. CircleArc(B, I, A) → q
  8. CircleArc(B, E, G) → e
  9. Intersect(e, i, 1) → H
  10. CircleSector(B, E, H) → k
  11. Mirror(C, j) → C'
  12. Mirror(H, j) → H'
  13. Angle(E, B, H) → α
  14. Dilate(B, If[0 < b ≤ 1, 1 - b, 0], D) → B'
  15. Segment(B, B') → l
  16. Segment(D, C) → m
  17. Angle(C, D, B) → β
  18. Mirror(D, j) → D'
  19. Mirror(C, j) → C'_1
  20. Segment(D', C'_1) → m'
  21. Angle(B, D, C') → γ
  22. Rotate(E, If[1 < b ≤ 2, ((b - 1) * α), α], B) → E'
  23. Mirror(E', j) → E''
  24. CircleSector(B, E, E') → r
  25. CircleSector(B, E'', E) → s
  26. Circle(B, 1) → d
  27. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C) → B'_1
  28. Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C'_1) → B'_2
  29. Segment(B, B'_1) → n
  30. Segment(B, B'_2) → t
  31. CircleArc(B, C', C) → c_1
  32. CircleSector(B, C, C') → d_1
  33. Polygon(B, D, C) → poly1, c_2, b_1, d_2
  34. Polygon(B, C', D) → poly2, d_3, b_2, c'
  35. Circle(B, A) → e_1
  36. Point(m') → K
  37. CircleSector(B, K, C) → g_1
  38. CircleSector(B, C, K) → h_1