We propose a new paradigm for reasoning over abstract argumentation frameworks where the trustworthiness of the agents is taken into account. In particular, we study the problems of computing the minimum trust degree τ^* such that, if we discard the arguments said only by agents whose trust degree is not greater than τ^*, a given set of arguments S (resp., argument a), that is not necessarily an extension (resp., (credulously) accepted) over the original argumentation framework, becomes an extension (resp., (credulously) accepted). Solving these problems helps reason on how the robustness of sets of arguments and single arguments depends on what is considered trustworthy or not. We thoroughly characterize the computational complexity of the considered problems, along with some variants where a different aggregation mechanism is used to decide the arguments to discard.