Constructing Tangent and Derivative of the Sine Function

This example shows how to construct the tangent line to the sine function at any chosen point and simultaneously display its derivative. ① It illustrates the geometric relationship between the sine graph, its tangent line, and the derivative. ② Key mathematical concepts include the sine function, trigonometric functions, tangent lines, derivatives, and the concept of instantaneous rate of change in calculus. ③ The construction uses GeoGebra commands Derivative and Line with objects f (sine function), a (slider for point), T (tangent line), f' (derivative function), v (vector), and t (tangent point). ④ It is suitable for high‑school or first‑year university students studying calculus and trigonometry.