Derivatives of Sine and Cosine: An Intuitive Interactive Exploration

① This GeoGebra example dynamically visualizes the derivative graphs of the sine and cosine functions, allowing learners to observe how the slope of the tangent line at each point relates to the original function. ② Core mathematical concepts include the geometric meaning of the derivative as the slope of a tangent, the derivative rules for trigonometric functions (d/dx sin x = cos x, d/dx cos x = -sin x), and properties such as periodicity, amplitude, and phase shift. ③ Construction highlights: using GeoGebra commands such as Point, Circle, Tangent, Intersect, and Vector, the applet builds a unit circle with a moving point, draws the tangent line, and uses buttons (button1, button2) and text (text1) to guide interactive exploration, tracing the derivative curve as the point moves. ④ Suitable for high school or introductory college calculus students, this resource supports classroom demonstration or self-study, with guiding questions that foster intuitive understanding of derivatives before formal rules are introduced.