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Graph Derivatives of sinx and cosx by David T

Graph Derivatives of sinx and cosx by David T
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2013-08-31 17:48
CalculusDerivativeGraphing
This example demonstrates how to graph the derivatives of the sine and cosine functions, sinx and cosx, and traces the derivative by moving the blue point. It involves core math concepts like derivatives, tangent lines, slopes, and trigonometric graphs. Constructed using GeoGebra commands/objects such as Point, Tangent, Slope, and Derivative. Suitable for high school students learning calculus to visually understand the relationship between functions and their derivatives.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Tangent(A, f) → t
  3. Slope(t) → s
  4. Derivative(f) → f'
  5. Point(g) → C
  6. Tangent(C, g) → b
  7. Slope(b) → slopeb
  8. Derivative(g) → g'

AI Drawing Prompt Reference

Graph the sine and cosine functions along with their derivatives. Move a point on the sine curve to draw its tangent line and display the slope, simultaneously plotting the derivative of the sine function. Perform similar actions on the cosine curve, showing its tangent line, slope, and derivative. Illustrate the relationship between the sine, cosine functions, and their derivatives to understand the geometric meaning of derivatives.
The prompt above was compiled from the original drawing commands and is for reference only.