Geometric construction of the tangent function from 0 to 2π

This example demonstrates how to visualize the tangent function over the interval [0, 2π] by turning an angle-based construction into an equivalent geometric relationship. It helps learners see how tan(θ) changes with the angle, highlighting periodicity and the way the function behaves across its definition gaps. The main math concepts are trigonometry—especially the tangent function—unit-circle/arc geometry, angle measurement, and the conversion between an angle and a corresponding linear geometric quantity. Construction approach in GeoGebra: key points and intersection points are created with Point and Intersect; CircleArc is used to place points along the circle for angles within 0 to 2π; Angle sets and labels the driving angle θ; Segment and Ray extend the relevant directions needed to form the tangent-related configuration; intersections between the rays/segments and other geometric elements determine the numeric geometric representatives of the tangent values. The construction uses multiple auxiliary points and an angle object (e.g., c, A, B, …, α, etc.) to represent the circle locations, auxiliary endpoints, and the angle parameter. Suitable for upper secondary and introductory university students for teaching/learning tangent properties and connecting geometric constructions with function graphs.