A novel electron distribution function is used in deriving analytic expressions for the synchrotron emissivity and absorption coefficient of relativistic loss cone and anti-loss cone distributions. Under most circumstances these expressions can be written in the form of the product of the corresponding expression for an isotropic plasma and a factor due to the anisotropy. Good agreement with numerical results is found under a wide variety of conditions. The new expressions give considerable insight into the variation of the emission and absorption with various physical parameters and enable the approximate forms of actual electron distributions to be inferred from the properties of the emitted radiation. It is shown that amplification of the synchrotron continuum is impossible for loss cones with Maxwellian distributions in energy, no matter how strong their anisotropy.