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Calculus - Derivative of Sine (Geometric Proof)

Calculus - Derivative of Sine (Geometric Proof)
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2016-12-27 05:28
TrigonometryCalculusDerivativeGeometric ConstructionSlider Animation
This example demonstrates the derivative of the sine function using a geometric approach. Key math concepts include derivatives, sine function, straight lines, special points, and intersection. Construction highlights the use of GeoGebra commands such as Intersect, Rotate, Segment, Angle, OrthogonalLine, Polygon, CircleArc, Point, Locus, Tangent, Ray, Distance, Midpoint, Center, and AngularBisector. Suitable for high school and above students studying calculus and trigonometry.

GeoGebra Commands & Parameters

  1. Intersect(c, xAxis, 2) → C_1
  2. Intersect(xAxis, yAxis) → B
  3. Rotate(C_1, θ, B) → T
  4. Segment(B, A) → f
  5. Segment(B, C_1) → g
  6. Rotate(A, Δθ, B) → D
  7. Segment(B, D) → h
  8. Angle(C_1, B, A) → α
  9. Angle(A, B, D) → β
  10. Intersect(c, i, 1) → D_1
  11. Segment(D_1, A) → j
  12. OrthogonalLine(D, j) → k
  13. Intersect(k, j) → E
  14. Segment(D, A) → l
  15. Segment(D, E) → m
  16. Intersect(c, n, 1) → F
  17. OrthogonalLine(F, j) → p
  18. Intersect(p, j) → G
  19. Segment(F, G) → q
  20. Segment(F, D) → r
  21. OrthogonalLine(A, g) → s
  22. Intersect(s, g) → C
  23. Polygon(B, C, A) → poly1, a_1, b_1, h_1
  24. Polygon(E, A, D) → poly2, a', e, a_2
  25. Angle(A, C, B) → γ
  26. Angle(A, E, D) → δ
  27. Angle(E, D, A) → ε
  28. CircleArc(B, A, D) → d
  29. Point(border) → P
  30. Locus(Q, P) → loc1
  31. Angle(B, A, C) → ϕ
  32. Tangent(A, c) → t, g_1
  33. Ray(B, D) → f_1
  34. Intersect(t, f_1) → I
  35. Angle(I, A, E) → ζ
  36. Distance(A, E) → o
  37. Midpoint(l) → J
  38. Center(d) → K
  39. Center(d) → L
  40. AngularBisector(D, B, A) → i_1
  41. Point(loc1) → M
  42. Intersect(t, i_1) → N
  43. Segment(D, A) → j_1
  44. Point(m) → H