Visualizing Trigonometric Derivatives: Tangent Slopes and Derivative Functions

① This example dynamically illustrates the derivatives of trigonometric functions (e.g., sine and cosine) by showing how the slope of a tangent line changes along the curve, thereby revealing the geometric meaning of the derivative function. ② Core mathematical concepts include the definition of the derivative, derivative rules for trigonometric functions, tangent slope as instantaneous rate of change, and the relationship between a function and its derivative graph. ③ Construction highlights: GeoGebra commands such as Point to place a moving point on the curve, Tangent to draw the tangent line, Element, Numerator, and Denominator to manipulate expressions, lists (deflist, defnames) to manage multiple functions, and text objects (text1, text2) to display derivative expressions and values, ultimately generating the derivative function g'. ④ Suitable for high school and early college students learning calculus, useful for understanding derivative concepts and trigonometric differentiation rules, and as a classroom demonstration tool for teachers.