Plasma wave observations are combined with the magnetometer measurements to investigate Titan's induced magnetosphere. Electric field emissions close to Titan are identified as upper hybrid resonance emissions and therefore can provide a density estimate of Titan's cold plasma. Some of Titan's flybys show a very strong asymmetry between two flybys performed in similar geographical conditions. Good examples are the Ta and Tb flybys, which have a similar trajectory in the Titan interaction coordinate system and even though they have the same illumination conditions, the density profiles present major differences. Thermal plasma observations are displayed for the nominal mission flybys in a draping coordinate system where the average ambient magnetic field, the ideal flow direction and the motional electric field correspond to the main axis of the system. This coordinate system organizes the cold plasma observations and provides information on the envelop of the induced magnetosphere and its global asymmetry.