Sine Compound Angle Identity Discovery (GeoGebra Activity Part 1)

This GeoGebra activity guides learners through a dynamic geometric construction to discover the sine compound angle identity sin(α+β) = sinα cosβ + cosα sinβ. By manipulating sliders for angles α and β, users observe how the sine value changes in relation to the constructed triangle and vector components. The construction employs Polygon, Angle, and Vector commands to create a dynamic configuration where reflecting and rotating triangles visually demonstrates the algebraic identity. Core trigonometry concepts include angle addition, unit circle relationships, and function transformation. Suitable for high school trigonometry courses, pre-calculus, or independent exploration of dynamic geometry and trigonometric identities. Teachers can use it to illustrate the connection between geometric construction and algebraic proof, while students gain intuitive understanding of how compound angles work.