Question: A museum curator is aligning two historical astrolabes represented by vectors $ eginpmatrix \cos lpha \ \sin lpha \endpmatrix $ and $ eginpmatrix \cos eta \ \sin eta \endpmatrix $ in the plane. If the cosine of the angle between them is $ rac13 $, and $ lpha + eta = 90^\circ $, find $ \sin(2lpha) $. - Portal da Acústica