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Sine and Cosine Challenge

Sine and Cosine Challenge
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2015-06-01 23:08
FunctionTrigonometryTransformation
This example demonstrates the graphs and properties of sine and cosine functions. It involves key mathematical concepts such as trigonometric functions, arithmetic mean, and symmetry. Using GeoGebra commands like Translate and Dilate, the graphs of sine and cosine functions are constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Numeric RginY(1)
  2. Numeric RginX(1)
  3. Numeric C(3)
  4. Numeric B(1.95)
  5. Numeric A(1)
  6. Numeric Translate_gLR(0)
  7. Numeric Translate_gUD(0)
  8. Numeric Dilate_gLR(0.99)
  9. Numeric Dilate_gUD(0.99)
  10. Numeric RfinY(1)
  11. Numeric RfinX(1)
  12. Numeric Translate_fLR(0)
  13. Numeric Dilate_fUD(0.99)
  14. Numeric a(0.95)
  15. Numeric b(0.999)
  16. Numeric c(-1)
  17. Numeric Translate_fUD(-0.01)
  18. Numeric Dilate_fLR(0.99)
  19. fL(x) = ((Dilate_fUD * RfinX) * ((a * (((RfinY * Dilate_fLR) * x) - Translate_fLR)) + b + Translate_fUD))
  20. fQ(x) = ((Dilate_fUD * RfinX) * ((a * (((RfinY * Dilate_fLR) * x) - Translate_fLR)^(2)) + (b * (((RfinY * Dilate_fLR) * x) - Translate_fLR)) + c + Translate_fUD))
  21. Boolean fLinear(false)
  22. Boolean fSin(false)
  23. Boolean fQuadratic(false)
  24. gL(x) = ((Dilate_gUD * RginX) * ((A * (((RginY * Dilate_gLR) * x) - Translate_gLR)) + B + Translate_gUD))
  25. gQ(x) = ((Dilate_gUD * RginX) * ((A * (((RginY * Dilate_gLR) * x) - Translate_gLR)^(2)) + (B * (((RginY * Dilate_gLR) * x) - Translate_gLR)) + C + Translate_gUD))
  26. Boolean gQuadratic(false)
  27. Boolean gCos(false)
  28. fA(x) = ((Dilate_fUD * RfinX) * ((a * sin((((RfinY * Dilate_fLR) * b) * x) - Translate_fLR)) + c + Translate_fUD))
  29. gA(x) = ((Dilate_gUD * RginX) * ((A * cos((((RginY * Dilate_gLR) * B) * x) - Translate_gLR)) + C + Translate_gUD))
  30. Boolean gLinear(false)
  31. f(x) = (fSin * fA(x))
  32. g(x) = (gCos * gA(x))