Investigating the Derivative of Sine: Tangent Slope and Function Graph

①This example dynamically shows the tangent line and its slope at a moving point on the sine function graph, visually demonstrating the geometric meaning of the derivative of sine—the rate of change of the tangent slope. ②Core mathematical concepts include derivatives, trigonometric functions, the fundamental fact that the derivative of sine is cosine, as well as tangent lines, slopes, and function graphs. ③Construction highlights: using GeoGebra commands Tangent to construct the tangent line to the sine function f at a movable point A, and Slope to compute the slope m of that tangent; a point B and text1 display the slope value, allowing users to drag A and observe how the slope changes with position. ④Suitable for high school or early college students learning calculus, to understand the definition of the derivative, the connection between tangent slope and rate of change, and as a classroom demonstration or self-guided exploration tool.