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Equivalent Sine and Cosine Graphs

Equivalent Sine and Cosine Graphs
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2017-05-11 03:16
FunctionTrigonometryParametric EquationGraphing
This example demonstrates the equivalence and transformation relationship between sine and cosine function graphs. It involves core math concepts like trigonometric functions, periodicity, phase difference, parametric equations, and coordinate geometry. GeoGebra commands and objects used include If statements, LaTeX for formulas, Slider Animation, Parametric Equation, and Locus. Suitable for high school mathematics teaching to help students understand trigonometric function graph transformations and the impact of parameters on function graphs.

GeoGebra Commands & Parameters

  1. If(abs(j) ≟ 4, Text[π], text10) → text11
  2. LaTeX(f, true, true) → text1
  3. If(a < 0, "-", "") → signA
  4. If(k < 0, "-", "") → signK
  5. If(c > 0, "-", "+") → signC
  6. If(c ≟ 0, "", signC) → text3
  7. If(c ≟ 0, "", text11) → text7
  8. If(absA ≟ 1, "", Text[absA]) → text6
  9. If(k ≟ 0, "", Text[absK]) → text5
  10. If(a < 0, "-", "") → signA_1
  11. If(k < 0, "-", "") → signK_1
  12. If(c > 0, "-", "+") → signC_1
  13. If(c ≟ 0, "", signC_1) → text3_1
  14. If(absA_1 ≟ 1, "", Text[absA_1]) → text6_1
  15. If(c ≟ 0, "", Text[absC_1]) → text7_1
  16. If(k < 0, "(", "") → text12
  17. If(k < 0, ")", "") → text13
  18. If((k < 0) ∧ c ≟ 0, "", "(") → text14
  19. If((k < 0) ∧ c ≟ 0, "", ")") → text15