This work is a natural continuation of our recent study devoted to the scattering of a plane incident
wave by a semi-infinite impedance sector. We develop an approach that enables us to compute different
components in the far-field asymptotics. The method is based on the Sommerfeld integral representation
of the scattered wave field, on the careful study of singularities of the integrand and on the asymptotic
evaluation of the integral by means of the saddle point technique. In this way, we describe the waves
reflected from the sector, diffracted by its edges or scattered by the vertex as well as the surface waves.
Discussion of the far-field in the so-called singular directions (or in the transition zones) is also addressed.