This paper is devoted to the study of a new family of distributions based on a sine transformation. In some situations, we show that the new family provides a suitable alternative to the so-called sine-G family of distributions, with the same number of parameters. Among others, some of its significant mathematical properties are derived, including shapes of probability density and hazard rate functions, asymptotes, quantile function, useful expansions, moments and moment generating function. Then, a special member with two parameters, using the inverse Weibull distribution as baseline, is introduced and investigated in detail. By considering this new distribution as a statistical model, the parameters are estimated via the maximum likelihood method. A simulation study is carried out to assess the performance of the obtained estimators. The applications on two real data sets are explored, showing the ability of the proposed model to fit various type of data sets.