Tracing Sine and Cosine with the Unit Circle

This example demonstrates how to trace the sine and cosine functions by using the unit circle: a rotating ray determines a point on the circle, and orthogonal projections translate that geometric position into sin(θ) and cos(θ). The key math concepts are trigonometric functions (sine and cosine), the unit-circle definition, angle-to-arc relationships, 2D vector interpretation via projections, and visual mapping that may resemble graphing/area/bar-style representations. Construction-wise, it leverages GeoGebra commands such as Point and Intersect to create essential points and intersection results, Segment to form connecting lines, OrthogonalLine to drop perpendiculars that produce the sin/cos projections, Angle to mark and control θ, and CircleArc to represent the corresponding circular arc. The construction organizes geometric objects (points, lines, arcs) together with on-screen text labels to communicate angle/function values. Ideal for secondary school and early undergraduate instruction on trigonometry, unit-circle reasoning, and connecting function graphs with geometric meaning.