We have observed and modeled the H-1 and F-19 solid-state nuclear spin relaxation process in polycrystalline 3-(trifluoromethyl)phenanthrene. The relaxation rates for the two spin species were observed from 85 to 300 K at the low NMR frequencies of omega/2 pi = 22.5 and 53.0 MHz where CF3 rotation, characterized by a mean time T between hops, is the only motion on the NMR time scale. All motional time scales (omega tau << 1 omega tau approximate to 1, and omega tau >> 1) are observed. The H-1 spins are immobile on the NMR time scale but are coupled to the F-19 spins via the unlike-spin dipole-dipole interaction. The temperature dependence of the observed relaxation rates (the relaxation is biexponential) shows considerable structure and a thorough analysis of Bloch-Wangsness-Redfield theory for this coupled spin system is provided. The activation energy for CF3 rotation is 11.5 +/- 0.7 kJ/mol, in excellent agreement with the calculation in a 13-molecule cluster provided in the companion paper where the crystal structure is reported and detailed ab initio electronic structure calculations are performed.