It is well-established in the existing literature that probability distributions significantly influence data modeling and the representation of real-world situations. In light of the considerable influence that probability distributions exert in various applied fields, this research is dedicated to the development of a novel probability distribution termed the sine–cosine generalized Rayleigh (SCG-Rayleigh) distribution. The SCG-Rayleigh distribution is formulated by merging the generalized Rayleigh distribution with two well-established trigonometric functions, specifically the sine and cosine functions. The SCG-Rayleigh distribution has been analyzed to derive specific properties related to its quantile function. Mathematical derivations have been performed to obtain the estimators for the parameters of this distribution. A simulation study has also been employed to assess these estimators. Moreover, the practical applicability and merits of the SCG-Rayleigh distribution are exemplified using two data sets from the engineering domain. The analysis of the engineering data sets involves a comparison of the SCG-Rayleigh distribution with various other distributions. According to the four statistical criteria utilized for decision-making, it is evident that the SCG-Rayleigh distribution demonstrates superior performance. The findings from the analysis suggest that the inclusion of trigonometric functions has markedly improved the optimality of the SCG-Rayleigh model.