  It is explained that any scalar field in $f(R,T)$ gravity model could present
a new subclass of the k-essence model for inflation. While the case of the
quintessence has been studied, there is an empty gap required to be filled by
investigating more types of field models. Here, we are aiming to partially fill
the gap and concentrate on the tachyon field. In this study, we explore the
phenomenon of tachyon inflation in the context of the alternative gravity
theory $f(R,T) = R + \eta T$. By applying slow-roll approximations, we examine
the model in detail for three different potentials: power-law, generalized
T-mode, and inverse hyperbolic cosh. Using observational data and Python
coding, we determine a range of values for the model's free parameters that
allow it to fit the data perfectly. In essence, this study provides a
comprehensive analysis of tachyon inflation in the $R + \eta T$ gravity theory,
offering new insights into this alternative framework and its potential to
explain tachyon inflation.
