We show that bimodal radio frequency spectra universally arise at intermediate temperatures in models of strongly interacting trapped Fermi gases. The bimodality is independent of superfluidity or pseudogap physics, depending only on the functional form of the equation of state-which is constrained by dimensional analysis at low temperatures and the virial expansion at high temperatures. In addition to these model independent results, we present a simple calculation of the radio frequency line shape of a highly polarized Fermi gas which uses energetic considerations to include final state interactions. While this model only qualitatively captures the line shapes observed in the experiments, it provides a conceptually clean and powerful technique for estimating the energy scales and how they vary with experimental parameters. © 2008 The American Physical Society.