We study the angular distribution of different spectral components of the terahertz emission from a single-color laser filament plasma. The opening angle of a terahertz cone is experimentally demonstrated to be proportional to the inverse square root of both plasma channel length and terahertz frequency in the non-linear focusing mode, whereas in the case of linear focusing this dependence breaks down. We also experimentally show that any conclusions of terahertz radiation spectral composition require the angle range from which it is collected to be specified.