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sin(75) & cos(75) activity

sin(75) & cos(75) activity
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2015-09-21 09:18
AngleTrigonometryGeometric Construction
This example demonstrates how to construct geometric figures to understand the values of sin(75) and cos(75). Core math concepts include trigonometric functions, angle calculations, and geometric constructions. Construction highlights involve commands like Ray, Intersect, OrthogonalLine, Point, Line, Segment, Angle, Rotate, and objects A, B, C, etc. Suitable for high school mathematics teaching to help students visually grasp the calculation and application of trigonometric functions.

GeoGebra Commands & Parameters

  1. Ray(A, C) → a
  2. Ray(A, D) → c
  3. Intersect(a, b) → E
  4. OrthogonalLine(E, a) → d
  5. Point(d) → F
  6. Intersect(d, c) → G
  7. Line(G, xAxis) → e
  8. Intersect(f, yAxis) → H
  9. Intersect(e, f) → I
  10. Intersect(b, e) → J
  11. Segment(G, E) → g
  12. Segment(I, G) → h
  13. Segment(G, J) → i
  14. Segment(J, E) → j
  15. Segment(E, B) → k
  16. Segment(I, A) → l
  17. Segment(A, E) → m
  18. Segment(A, G) → n
  19. Intersect(b, c) → M
  20. Segment(A, B) → q
  21. Angle(A, I, G) → ζ
  22. Rotate(B, 45*°, A) → B'
  23. Angle(B, A, B') → α
  24. Ray(A, B') → p
  25. Rotate(B', 30*°, A) → B''
  26. Angle(B', A, B'') → β
  27. Ray(A, B'') → r
  28. Intersect(h, r) → K
  29. OrthogonalLine(K, m) → s
  30. Intersect(s, m) → L
  31. OrthogonalLine(L, q) → t
  32. Intersect(q, t) → N
  33. Intersect(t, h) → O
  34. Intersect(t, i) → P
  35. Segment(I, K) → a_1
  36. Segment(K, P) → b_1
  37. Segment(P, L) → c_1
  38. Segment(L, N) → d_1
  39. Segment(N, A) → e_1
  40. Segment(A, K) → f_1
  41. Segment(K, L) → g_1
  42. Angle(K, L, A) → α_1
  43. Angle(I, P, N) → β_1
  44. Angle(P, N, A) → γ
  45. Segment(A, L) → h_1
  46. Angle(P, L, K) → δ
  47. Angle(I, K, A) → ε

AI Drawing Prompt Reference

Draw a right triangle with angle A as the right angle, angle B as 45 degrees, and angle C as 30 degrees. Construct the geometric representation of sin(75) and cos(75) through rotations and intersections. Start by drawing two rays AB and AC, then construct angles B and C through rotations, and finally use intersections and rays to construct the triangle's sides and angles, illustrating the geometric meaning of trigonometric functions.
The prompt above was compiled from the original drawing commands and is for reference only.