The impact of electromagnetic (thermal) radiation on the dispersive low-frequency waves is examined in a radiative dusty magnetoplasma. For this purpose, a magneto-hydrodynamic model along with the Maxwell equations is employed to describe the three-component radiative dusty plasma that contains inertialess electrons, dynamical positive ions and negatively charged static dust particulates. The behavior of the electrostatic and electromagnetic waves significantly changes in a plasma medium when a radiation pressure is taken into consideration, as compared to the waves in vacuum. After seeking a plane wave solution, a general dispersion relation is obtained to investigate different limiting cases of the low-frequency modes propagating parallel, perpendicular and oblique to the external magnetic field direction both analytically and numerically. The calculations reveal that the usual thermal and acoustic speeds (cT, ca) do not remain constant even if the temperature is kept constant, because of the radiation pressure
which strongly depends on the equilibrium number density as well. The present results may prove a useful understanding for the new features of the dispersive dust-ion-acoustic and compressional Alfven waves in astrophysical dusty magnetoplasmas.