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This paper proposes the concept, analysis and design of a sinusoidally modulated graphene leaky-wave antenna with beam scanning capabilities at a fixed frequency. The antenna operates at terahertz frequencies and is composed of a graphene sheet transferred onto a back-metallized substrate and a set of polysilicon DC gating pads located beneath it. In order to create a leaky-mode, the graphene surface reactance is sinusoidally modulated via graphene's field effect by applying adequate DC bias voltages to the different gating pads. The pointing angle and leakage rate can be dynamically controlled by adjusting the applied voltages, providing versatile beamscanning capabilities. The proposed concept and achieved performance, computed using realistic material parameters, are extremely promising for beamscanning at THz frequencies, and could pave the way to graphene-based reconfigurable transceivers and sensors.