In this paper, we introduce a new trigonometric family of continuous distributions called the sine Kumaraswamy-G family of distributions. It can be presented as a natural extension of the well-established sine-G family of distributions, with new perspectives in terms of applicability. We investigate the main mathematical properties of the sine Kumaraswamy-G family of distributions, including asymptotes, quantile function, linear representations of the cumulative distribution and probability density functions, moments, skewness, kurtosis, incomplete moments, weighted moments and order statistics. Then, we focus our attention on a special member of this family called the sine Kumaraswamy exponential distribution. The statistical inference for the related parametric model is explored by using the maximum likelihood method. Among others, asymptotic confidence intervals and likelihood ratio test for the parameters are discussed. A simulation study is performed under varying sample size to assess the performance of the model. Finally, applications to two practical data sets are presented to illustrate its potentiality and robustness.