Nonresonant x-ray magnetic scattering has been used to study the magnetic structure of multiferroic TbMnO3 in its ferroelectric phase. Circularly polarized x rays were combined with full polarization analysis of the scattered beam to reveal important new information on the magnetic structure of this canonical multiferroic. An applied electric field is shown to create essentially a single magnetic domain state in which the cycloidal order on the Mn sublattice rotates either clockwise or anticlockwise depending on the sign of the field. It is demonstrated how this technique provides sensitivity to the absolute sense of rotation of the Mn moments and to components of the ordering on the Tb sublattice and phase shifts that earlier neutron diffraction experiments could not resolve.