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Demonstration of Sine of Angle Sum

Demonstration of Sine of Angle Sum
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2019-03-27 20:22
FunctionTrigonometryCoordinate GeometryGeometric Construction
This example dynamically illustrates the relationship between the sine of the sum of two angles and the individual sines of those angles. It involves core mathematical concepts such as trigonometric functions, angle sum formulas, and analytical geometry. Construction highlights include using GeoGebra commands like CurveCartesian for curves, Point for points, Intersect for intersections, Segment for segments, OrthogonalLine for perpendicular lines, Angle for angle measurement, Polygon for polygons, Line for lines, and Vector for vectors. It is suitable for high school mathematics students to learn and understand the properties of trigonometric functions, as well as for introductory calculus teaching.

GeoGebra Commands & Parameters

  1. CurveCartesian(cos(t), sin(t), t, 0, π / 2) → a
  2. Point(a) → A_1
  3. Point(a) → B
  4. Intersect(xAxis, yAxis) → O
  5. Segment(O, A_1) → f
  6. Segment(O, B) → g
  7. OrthogonalLine(B, f) → h
  8. Intersect(h, f) → A
  9. OrthogonalLine(B, xAxis) → i
  10. OrthogonalLine(A, xAxis) → j
  11. OrthogonalLine(B, j) → k
  12. Intersect(xAxis, i) → E
  13. Intersect(xAxis, j) → F
  14. Intersect(k, j) → G
  15. Segment(B, E) → l
  16. Segment(B, A) → m
  17. Segment(G, F) → n
  18. Segment(B, G) → p
  19. Angle(E, O, A) → α
  20. Angle(A, O, B) → β
  21. Angle(B, A, O) → γ
  22. Polygon(C, I, H) → t1, h_1, c, d
  23. Angle(I, C, H) → δ
  24. Angle(F, O, B) → ε
  25. Line(L, f) → q
  26. Line(L, g) → r
  27. Point(q) → M
  28. Line(M, m) → s
  29. Intersect(r, s) → N
  30. Segment(L, N) → t
  31. Segment(L, M) → b
  32. Segment(M, N) → e
  33. Angle(M, L, N) → ζ
  34. Segment(P, Q) → f_1
  35. Segment(Q, R) → g_1
  36. Segment(S, R) → i_1
  37. Angle(G, A, B) → η
  38. Segment(T, U) → j_1
  39. Segment(T, U) → k_1
  40. Segment(U, V) → l_1
  41. Segment(V, T) → m_1
  42. Angle(U, V, T) → θ
  43. Segment(W, Z) → n_1
  44. Segment(C_1, B_1) → p_1
  45. Segment(Z, C_1) → q_1
  46. Point(xAxis) → F_1
  47. Point(xAxis) → G_1
  48. Polygon(D_1, E_1, F_1, G_1) → c1, d_1, e_1, r_1, s_1
  49. Point(d_1) → H_1
  50. Vector(H_1, I_1) → u