Obtaining the wrapped phase is a crucial step in fringe projection profilometry. However, reliably and efficiently extracting the wrapped phase from fringe patterns under non-ideal conditions remains a challenging problem. Neural networks have demonstrated higher robustness under non-ideal conditions; however, they struggle to handle abrupt data at the edge of the phase cycle when directly predicting the wrapped phase. To address this issue, we propose “trigonometric phase net (TPNet),” an approach that leverages the distribution characteristics of wrapped phase data. TPNet uses a neural network to predict the wrapped phase in the form of sine and cosine values; the wrapped phase is then calculated using the a tan function. This approach not only avoids the direct processing of abrupt data by the neural network but also facilitates network convergence due to its similar distribution law as fringe patterns. We also introduce a new loss function, Loss_sincos, which is designed to align with the sine and cosine function distribution of the network’s output. This loss function improves the accuracy of the neural network in indirectly predicting the wrapped phase. Our experiments demonstrate that TPNet can accurately extract the wrapped phase from single frame fringe patterns under non-ideal conditions.