We report accurate coupled-channel quantum calculations of state-to-state and degeneracy-averaged differential cross sections for the rotationally inelastic collision Ar Jr HF(v(i) = 0, j(i) = 0, m(i) = 0) --> Ar + HF(v(f) = 0, j(f), m(f)), where v(i), j(i), m(i) and v(f), j(f), m(f) are initial and final vibrational, rotational, and helicity quantum numbers, respectively. The calculations have been performed at eight collision energies and assume that HF is a rigid rotator. Structure in the differential cross sections is analyzed using the unrestricted version of nearside-farside (NF) theory. The NF theory decomposes the partial wave series (PWS) for the helicity scattering amplitude into two subamplitudes, one N, the other F. This is the first application of NF theory to an atom-heteronuclear molecule inelastic collision. It is demonstrated that the NF technique provides a clear physical interpretation of the angular scattering, except sometimes for scattering angles, theta, close to 0 degrees and 180 degrees. It is also shown that a resummation of the PWS can improve the usefulness of the NF technique, when the N and F cross sections possess small oscillations. The resummation procedure exploits recurrence properties of reduced rotation matrix elements to extract a factor (alpha + beta cos theta)(-1) from the PWS, where alpha and beta are constants. Criteria for choosing alpha and beta so as to obtain a physically meaningful NF decomposition are discussed.