This research introduces a novel extension of the well-established inverted exponentiated Weibull distribution. By incorporating a trigonometric sine function, we develop the sine-inverted exponentiated Weibull (SIEW) distribution, a flexible model capable of capturing a wide range of data patterns. The SIEW distribution exhibits versatility in modeling data with increasing, decreasing, reversed J-shaped, and upside-down shaped hazard rates, making it suitable for various real-world applications. To comprehensively understand the SIEW distribution, we delve into its key statistical properties and compute entropy measures such as Rényi and Tsallis. For parameter estimation, we employ both classical maximum likelihood and Bayesian estimation procedures, considering symmetric and asymmetric loss functions. Recognizing the computational challenges inherent in Bayesian estimation, we implement Markov Chain Monte Carlo techniques with independent gamma priors. The performance of the SIEW distribution is rigorously assessed through extensive simulation studies and real-world data analysis. By comparing the SIEW model to existing alternatives, we demonstrate its superior flexibility and effectiveness in modeling complex data structures. This study contributes to statistical literature by providing a new and adaptable tool for data analysis across various domains.