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Sinusoidal Transformations: Sine and Cosine

Sinusoidal Transformations: Sine and Cosine
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2019-01-16 09:23
TrigonometryDerivativeTransformation
This example demonstrates transformations of sine and cosine functions. Key mathematical concepts include trigonometric functions, derivatives, and geometric transformations. By adjusting parameters, you can observe changes in the sine and cosine function graphs. GeoGebra commands used include functions, slider animations, and geometric transformations. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Numeric a(1.0)
  2. Numeric c(0.0015)
  3. Numeric b(1.0)
  4. c / π
  5. Numeric d(0.0)
  6. f(x) = (a * sin((b * x) + c)) + d
  7. g(x) = (a * cos((b * x) + c)) + d
  8. Boolean e(true)
  9. Boolean h(false)

AI Drawing Prompt Reference

Draw the graphs of sine and cosine functions, and observe how they change by adjusting parameters a, b, c, and d. a controls the amplitude, b controls the period, c controls the phase shift, and d controls the vertical shift. Start with the sine function, then draw the cosine function.
The prompt above was compiled from the original drawing commands and is for reference only.