Analytical calculation of the solid angle subtended by a circular disc detector at a point cosine source

We derive analytical expressions for the solid angle subtended by a circular disc at a point source with cosine angular distribution ( f( μ)= μ/ π) under the sole condition that the disc lies in the half-space illuminated by the source ( μ⩾0). The expressions are given with reference to two alternative coordinate systems (S and S'), S being such that the z-axis is parallel to the symmetry axis of the disc and S' such that the z'-axis is aligned with the source direction. Sample plots of the expressions are presented.