We report on polarized infrared reflectivity measurements of multiferroic, monoclinic MnWO4 between 10 K and 295 K. All five non-vanishing components of the dielectric tensor have been determined in the frequency range of the phonons. All infrared-active phonon modes (7 Au modes and 8 Bu modes) are unambiguously identified. In particular the strongest Bu modes have been overlooked in previous studies, in which the monoclinic symmetry was neglected in the analysis. The combined analysis of reflectance data measured in different experimental geometries (Rac and Rp) is particularly helpful for a proper identification of the Bu modes. Using a generalized Drude-Lorentz model, we determine the temperature dependence of the phonon parameters, including the orientation of the Bu modes within the ac plane. The phonon parameters and their temperature dependence were discussed controversially in previous studies, which did not include a full polarization analysis. Our data do not confirm any of the anomalies reported above 20 K. However, in the paramagnetic phase we find a drastic reduction of the spectral weights of the weakest Au mode and of the weakest Bu mode with increasing temperature. Below 20 K, the parameters of the Au phonon modes for E b show only subtle changes, which demonstrate a finite but weak coupling between lattice dynamics and magnetism in MnWO4. A quantitative comparison of our infrared data with the quasi-static dielectric constant ε b yields a rough estimate for the oscillator strength ∆εem 0.02 of a possible electromagnon for E b. Furthermore, we report on a Kramers-Kronig-consistent model which is able to describe non-Lorentzian line shapes in compounds with monoclinic symmetry.