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Interactive Trigonometric Equation Solving and Graphing

Interactive Trigonometric Equation Solving and Graphing
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2017-01-29 06:36
FunctionTrigonometryInequalitySlider AnimationGraphing
This GeoGebra example demonstrates the graphical solution of trigonometric equations such as sin(x)=k through an interactive interface. Core mathematical concepts include trigonometric functions, equation solving, intersections of function graphs, and the influence of parameters on solutions. Construction highlights: using commands like Element, Textfield, Point, Vector, and Intersect, it builds sliders (k), input boxes (inputBox1/2/3), function graphs (trig), and intersection points (C, R) to dynamically show how the number and positions of solutions change as parameters vary. Suitable for high school or pre-university students learning trigonometric equations, function graphing, and numerical methods, as well as for classroom demonstrations or self-exploration of parameter effects.

GeoGebra Commands & Parameters

  1. Element(trl, fnum) → trig
  2. Element(atrl, fnum) → atrig
  3. Element(atrl2, fnum) → atrig2
  4. Textfield(B) → inputBox1
  5. Textfield(s) → inputBoxf
  6. Point(yAxis) → A_x
  7. Vector(K, s_{inv}D) → w
  8. Vector(s_{inv}D, m_{invSinvD}) → z
  9. Vector(m_{invSinvD}, q_{inv+}) → d
  10. Vector(q_{inv+}, I) → h_1
  11. Textfield(C) → inputBox2
  12. Textfield(k) → inputBox3
  13. Textfield(A) → inputBox4
  14. Textfield(B) → inputBox5
  15. Textfield(s) → inputBox6
  16. Vector(m_{invSinvD}, P_2) → u
  17. Vector(P_2, J) → j
  18. Vector(I, E) → v
  19. Vector(J, D) → c
  20. Textfield(B) → inputBox7
  21. Vector(A_x, F) → m
  22. Vector(F, G) → n
  23. Vector(G, H) → p
  24. Vector(H, L) → q
  25. Vector(L, M) → r
  26. Textfield(D_n) → inputBox8
  27. Vector(A_x, M) → t
  28. Vector(K, E) → u_1
  29. Vector(K, D) → v_1
  30. Intersect(trf, a_1, (10.348809000348663, 4.000000000468522)) → N