Tangent Function Geometric Construction and Limit Demonstration

This GeoGebra example demonstrates the geometric construction and limit behavior of the tangent function. It explores how the tangent function's graph transforms under geometric dilation and parameter changes, illustrating the connection between trigonometric functions and geometric figures such as trapezoids and sectors. The construction uses fundamental GeoGebra commands including Point, Ray, Circle, Segment, Rotate, Angle, CircleArc, CircleSector, Area, and Circumference, along with numerous points, angles, and area calculations to model the function's geometric properties. It is suitable for high school function modules and introductory calculus courses, helping students visualize the geometric meaning of tangent functions and limit concepts.