The Addition Formula for Sine and Cosine: Geometric Proof and Illustration

This GeoGebra example provides a dynamic geometric proof and illustration of the addition (and subtraction) formulas for sine and cosine. It demonstrates how the identities sin(α±β) and cos(α±β) arise from the rotation of points on the unit circle and the projection of coordinates. The construction uses a Circle to define the unit circle, Point and Intersect to place key vertices, Line, OrthogonalLine, and Segment to build auxiliary right triangles, and Angle to mark the involved angles α, β, and their combinations. Midpoint and Text objects are used to label segments and display the derived relationships. The example emphasizes geometric construction and transformation (rotation, translation) as a visual proof tool. It is suitable for high school or introductory college students learning trigonometric identities, and serves as an interactive classroom demonstration to bridge geometric intuition and algebraic formulas.