Unit Circle Trigonometry Introduction: Geometry of Angles

This example demonstrates, via constructions on the unit circle, how an angle corresponds to coordinates and hence to trigonometric quantities like sine and cosine. The central ideas are the unit circle definition, the geometric interpretation of trig ratios, and the use of orthogonality to relate points to right angles. Key construction steps use GeoGebra commands and objects reflected in the build summary: Intersect to compute important intersection points (e.g., A, B, C, D, etc.), Point to create key loci points, Ray/Line/Segment to form rays, lines, and segments that serve as geometric scaffolding, Circle to draw the unit circle, OrthogonalLine to drop perpendiculars that encode right-angle relationships, and Angle to mark angles (α, β) for the correspondence between angle and coordinates. Text objects (text1–text10, text2, text6, etc.) are used for labeling. Suitable for secondary school through early undergraduate use, especially for lessons introducing unit-circle trig and geometry-based visualization.