Funky Functions of the Unit Circle: Dynamic Trigonometry and Geometry

This GeoGebra example dynamically illustrates the relationships between the unit circle and trigonometric functions such as sine, cosine, tangent, cotangent, and secant, by linking circle points, coordinates, and segment lengths. It integrates additional geometric concepts including tree diagrams, scalene triangles, incircles, linear equations, and percentages, making it a rich exploratory tool. Core mathematical concepts include the unit circle definition of trigonometric functions, angle measurement, geometric transformations (rotation), and function graphing. The construction uses GeoGebra commands such as Intersect, Circle, Point, Angle, If, Line, Segment, Rotate, and Distance, with objects like snap, r, A, c, B, Q, α, test, tolerance, and various derived points. A slider controls the angle, and the values of sinθ, cosθ, tanθ, cotθ, and secθ are computed in real time, with conditional logic (If) and tolerance for dynamic updates. This resource is suitable for high school and college-level students learning trigonometry, unit circle concepts, and function visualization, helping them grasp periodicity and geometric interpretations.