<p>Recently, a trigonometric transformation of the distribution function has become an interesting way to provide versatility and adaptability in data modeling as the parameter oscillates with a change in its value, and the periodic function controls the behavior of the distribution. The development of the marginals is the key point in this paper to enhance modeling bivariate data without accumulation of new parameters by defining trigonometric marginals using Sin-transformation and then employing it in the Farlie–Gumbel Morgenstern (FGM) Copula Model. The proposed model is named by Morgenstern Sin Generalized Exponential (MSGE) distribution. The statistical and reliability properties of MSGE are derived mathematically. Furthermore, point estimation is discussed and compared via three different methods; Maximum Likelihood (MLE), Method of Moments (MME), and Inference Function for Margins (IFM) method, and simulation schemes with comparisons are performed to examine the unbiasedness and efficiency of parameter estimates. Finally, Economics, medicine, and environmental real-life data applications were investigated to compare the goodness-of-fit of the introduced model. The applications describe climate changes, gross domestic product, and diabetes indicators. The results exhibited the performance and flexibility of the MSGE model without overloading extra parameters. MSGE presents a good competitor in fitting multidisciplinary lifetime data compared with other well-known bivariate models.</p>