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Solving Simple Sine Equations

Solving Simple Sine Equations
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2012-10-01 23:46
FunctionTrigonometryGeometric ConstructionSlider Animation
This example shows how to solve simple sine equations by changing slider values. Users can dynamically adjust parameters to see how the sine graph intersects with a given line, and use geometric constructions involving distances and vectors to find the equation's solutions. The core mathematical concepts include the graphical properties of sine functions, geometric interpretation of equation roots, orthogonal relationships between vectors and lines, and distance and intersection calculations. The construction employs GeoGebra commands such as OrthogonalLine to draw perpendiculars, Intersect to locate intersections, Segment to create line segments, Vector to represent direction, and Distance to measure lengths, all controlled by sliders for variables a, b, c, etc. It is suitable for high‑school students learning trigonometric equation solving and for university courses covering elementary mathematical methods.

GeoGebra Commands & Parameters

  1. OrthogonalLine(K, c) → d
  2. OrthogonalLine(L, c) → e
  3. OrthogonalLine(J, c) → g
  4. OrthogonalLine(I, c) → h
  5. OrthogonalLine(H, c) → i
  6. OrthogonalLine(G, c) → j
  7. OrthogonalLine(A, c) → k
  8. OrthogonalLine(E, c) → l
  9. OrthogonalLine(D, c) → m
  10. OrthogonalLine(F, c) → n
  11. OrthogonalLine(C, c) → p
  12. OrthogonalLine(B, c) → q
  13. Intersect(d, r) → M
  14. Intersect(e, r) → N
  15. Intersect(g, r) → O
  16. Intersect(h, r) → P
  17. Intersect(i, r) → Q
  18. Intersect(j, r) → R
  19. Intersect(k, r) → S
  20. Intersect(l, r) → T
  21. Intersect(m, r) → U
  22. Intersect(n, r) → V
  23. Intersect(p, r) → W
  24. Intersect(q, r) → Z
  25. Segment(K, M) → s
  26. Segment(L, N) → t
  27. Segment(J, O) → a_1
  28. Segment(I, P) → b_1
  29. Segment(H, Q) → c_1
  30. Segment(G, R) → d_1
  31. Segment(A, S) → e_1
  32. Segment(E, T) → f_1
  33. Segment(D, U) → g_1
  34. Segment(F, V) → h_1
  35. Segment(C, W) → i_1
  36. Segment(B, Z) → j_1
  37. OrthogonalLine(A_1, c) → k_1
  38. Intersect(r, k_1) → B_1
  39. Segment(A_1, B_1) → l_1
  40. Vector(C_1, N_1) → u
  41. Vector(E_1, Q_1) → v
  42. Vector(F_1, R_1) → w
  43. Vector(G_1, S_1) → z
  44. Vector(H_1, T_1) → u_1
  45. Vector(I_1, U_1) → v_1
  46. Vector(J_1, V_1) → w_1
  47. Vector(P_1, W_1) → z_1
  48. Vector(K_1, Z_1) → m_1
  49. Vector(L_1, A_2) → n_1
  50. Vector(M_1, B_2) → p_1
  51. Vector(D_1, C_2) → q_1
  52. Vector(O_1, D_2) → r_1
  53. Distance(C_1, N_1) → distanceC1N1
  54. Distance(Q_1, E_1) → distanceQ1E1
  55. Distance(F_1, R_1) → distanceF1R1
  56. Distance(S_1, G_1) → distanceS1G1
  57. Distance(H_1, T_1) → distanceH1T1
  58. Distance(U_1, I_1) → distanceU1I1
  59. Distance(J_1, V_1) → distanceJ1V1
  60. Distance(W_1, P_1) → distanceW1P1
  61. Distance(K_1, Z_1) → distanceK1Z1
  62. Distance(A_2, L_1) → distanceA2L1
  63. Distance(M_1, B_2) → distanceM1B2
  64. Distance(C_2, D_1) → distanceC2D1
  65. Distance(O_1, D_2) → distanceO1D2