Sine Approximation via Rounding on the Unit Circle

This example demonstrates how approximation and rounding can be applied in a unit-circle-based setting to obtain computed results, and how the outcomes can be summarized with hit/miss statistics. Key mathematics includes circles and the unit circle, trigonometry (in particular geometric correspondence related to sine), approximation/rounding error, and basic probability & statistics style aggregation using counts of successes and failures. Construction and implementation follow the GeoGebra workflow: Random and Sequence generate randomized angle/point samples (objects such as p, a_1…a_7, and lists lista1–lista4), Circle together with Polygon (and corner construction) build the unit-circle reference and geometric region (objects B, C, A, D, polígono1, Circle), and Textfield/buttons provide interactive input and feedback (p2campoDeTexto1/2, p2botón1, and text objects for “well/incorrect” messages). Finally, counters like total, aciertos, and fallos accumulate results and display them (along with intermediate variables such as r1/r2 and derived points p2c1/p2c2). Suitable for secondary school to introductory undergraduate use, especially for teaching function–geometry connections, numerical error awareness, and statistical comparison through repeated trials.