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Study Graphs of Trigonometric Functions by Mathguru

Study Graphs of Trigonometric Functions by Mathguru
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2013-01-15 15:41
FunctionTrigonometryDerivativeGraphing
This example demonstrates how to use GeoGebra to draw and study the graphs of two trigonometric functions with upper and lower limits. Key math concepts include trigonometric functions, geometric transformations, and function graphing. Construction highlights involve commands and objects like If, Function, Derivative, RemoveUndefined, Point, Textfield, Sequence, Asymptote, Intersect, Distance, Vector, Midpoint. Suitable for high school and above students for self-study and exploration of trigonometric properties.

GeoGebra Commands & Parameters

  1. If(angledegree, lowerlimit_d * π / 180, lowerlimit_r) → lowerlimit
  2. If(angledegree, upperlimit_d / 180, upperlimit_r) → upperlimit
  3. Function(g_{hidden}, lowerlimit * π, upperlimit * π) → g
  4. Derivative(g_{hidden}) → g'
  5. RemoveUndefined(Sequence[x(Root[g', i]), i, -31.41593, 31.41593, 0.31416]) → sincosturningptslistg
  6. Function(f_{hidden}, lowerlimit * π, upperlimit * π) → f
  7. Derivative(f_{hidden}) → f'
  8. RemoveUndefined(Sequence[x(Root[f', i]), i, -31.41593, 31.41593, 0.31416]) → sincosturningptslistf
  9. Point(g) → P_{02}
  10. Point(f) → P_{01}
  11. If(Length[sincosturningptslistg] > 0, false, true) → gchecktanfunction2
  12. Derivative(g') → g''
  13. Derivative(f') → f''
  14. If(Length[sincosturningptslistf] > 0, false, true) → fchecktanfunction1
  15. Textfield(f_{hidden}) → inputBox1
  16. Textfield(g_{hidden}) → inputBox4
  17. Sequence(Text[i + "°", (π / 180 * i - 0.05, -0.3)], i, 0, 1080, 90) → listxaxisdegreesby90
  18. If(fchecktanfunction1 ≟ false, (y(Max[f, lowerlimit * π, upperlimit * π * 10]) + y(Min[f, lowerlimit * π, upperlimit * π * 10])) / 2, meanline_{1fortan}) → meanline_1
  19. If(gchecktanfunction2 ≟ false, (y(Max[g, lowerlimit * π, upperlimit * π * 10]) + y(Min[g, lowerlimit * π, upperlimit * π * 10])) / 2, meanline_{2fortan}) → meanline_2
  20. Textfield(h_{hidden}) → inputBox5
  21. Function(h_{hidden}, lowerlimit * π, upperlimit * π) → h
  22. Function(meanline_1, lowerlimit * π, upperlimit * π) → f_{meanline1}
  23. Function(meanline_2, lowerlimit * π, upperlimit * π) → g_{meanline2}
  24. Textfield(lowerlimit_d) → inputBox6
  25. Textfield(upperlimit_d) → inputBox7
  26. Function(0, lowerlimit * π, upperlimit * π + 1) → h_{x-axis}
  27. Textfield(upperlimit_r) → inputBox3
  28. Textfield(lowerlimit_r) → inputBox2
  29. Sequence(Text[FractionText[i] + "π", (π * i - 0.15, -0.1), true, true], i, lowerlimit + xunitdistance, upperlimit, xunitdistance) → listxaxisradianlabel
  30. Sequence((i, 0), i, lowerlimit * π, upperlimit * π, xunitdistance * π) → listxaxisticks
  31. Sequence(abs(f(i)), i, lowerlimit * π, upperlimit * π, 0.01) → valuestanfunction
  32. Asymptote(f) → list5
  33. Asymptote(Function[g, lowerlimit * π, upperlimit * π]) → list6
  34. If(fchecktanfunction1 ≟ false, y(Max[f, lowerlimit * π, upperlimit * π * 10]), 0) → maxline_1
  35. If(fchecktanfunction1 ≟ false, y(Min[f, lowerlimit * π, upperlimit * π * 10]), 0) → minline_1
  36. Function(maxline_1, lowerlimit * π, upperlimit * π) → f_{maxline1}
  37. Function(minline_1, lowerlimit * π, upperlimit * π) → f_{minline1}
  38. Intersect(f_{maxline1}, vertline1) → A_1
  39. Intersect(f_{minline1}, vertline1) → B_1
  40. Intersect(f_{meanline1}, vertline1) → C_1
  41. Distance(A_1, C_1) → distanceA1C1
  42. Vector(C_1, A_1) → u_1
  43. Vector(C_1, B_1) → v_1
  44. Midpoint(A_1, C_1) → M_{A1C1}
  45. Midpoint(B_1, C_1) → M_{C1B1}
  46. If(gchecktanfunction2 ≟ false, y(Max[g, lowerlimit * π, upperlimit * π * 10]), 0) → maxline_2
  47. If(gchecktanfunction2 ≟ false, y(Min[g, lowerlimit * π, upperlimit * π * 10]), 0) → minline_2
  48. Function(maxline_2, lowerlimit * π, upperlimit * π) → g_{maxline1}
  49. Function(minline_2, lowerlimit * π, upperlimit * π) → g_{minline1}
  50. Intersect(g_{maxline1}, vertline2) → A_2
  51. Intersect(g_{minline1}, vertline2) → B_2
  52. Intersect(g_{meanline2}, vertline2) → C_2
  53. Midpoint(A_2, C_2) → M_{A2C2}
  54. Midpoint(B_2, C_2) → M_{B2C2}
  55. Distance(A_2, C_2) → distanceAC
  56. Vector(C_2, A_2) → u_2
  57. Vector(C_2, B_2) → v_2
  58. If(fchecktanfunction1, tancyclesf, sincoscycles1) → cycles1
  59. If(gchecktanfunction2, tancyclesg, sincoscycles2) → cycles2
  60. Intersect(g, vertline3, (0, -2)) → P_1
  61. Midpoint(P_1, Q_1) → M_{P1Q1}
  62. Vector(M_{P1Q1}, P_1) → u_{p1l}
  63. Vector(M_{P1Q1}, Q_1) → u_{p1r}
  64. Intersect(f, vertline4, (0.37243505127654164, 1.2055278889599705)) → P_2
  65. Midpoint(P_2, Q_2) → M_{P2Q2}
  66. Vector(M_{P2Q2}, Q_2) → u_{p2r}
  67. Vector(M_{P2Q2}, P_2) → u_{p2l}
  68. Derivative(f'') → f'''
  69. Derivative(g'') → g'''
  70. Sequence(Text[i + "°", (π / 180 * i - 0.15, -0.55)], i, lowerlimit * 180 + 180 * xunitdistance, upperlimit * 180, 180 * xunitdistance) → listxaxisdegreesby45

AI Drawing Prompt Reference

Draw the graphs of two trigonometric functions within specified upper and lower limits. Plot the functions and their derivatives, then identify the turning points as the roots of the derivatives. Calculate and draw the mean lines for each function, along with horizontal lines at the maximum and minimum values. Add coordinate axes, degree and radian tick marks, and asymptotes for the function graphs.
The prompt above was compiled from the original drawing commands and is for reference only.