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Derivative of sin(x)

Derivative of sin(x)
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2016-04-22 01:49
TrigonometryCalculusDerivativeGeometric ConstructionGraphing
This example demonstrates the derivative of the sine function y=sin(x) and its geometric interpretation, visually showing the variation of the slope of the tangent line through dynamic construction. Core mathematical concepts include the definition of derivatives, properties of trigonometric functions, and slope calculation of tangents. GeoGebra commands like Point, Tangent, and Slope are used, with objects such as point A, variable a, slope m, and point B to construct the relationship between the tangent and the derivative. Suitable for high school calculus teaching to understand the geometric meaning of derivatives and the dynamic correlation between function graphs.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Tangent(A, f) → a
  3. Slope(a) → m

AI Drawing Prompt Reference

Draw the graph of the sine function y=sin(x), take a point on the curve, draw the tangent line at that point, and display the slope of the tangent line to dynamically show the variation of the slope, visually interpreting the derivative and geometric meaning of the sine function.
The prompt above was compiled from the original drawing commands and is for reference only.