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Trigonometric distributions have recently been emphasized due to it applicability and relevance for modeling different phenomena. This article contributes to the existing literature on trigonometric family by introducing and investigating new trigonometric family of distribution which is developed by compounding the cosine family of distribution with Marshall-olkin family of distribution to form a new Cosine Marshall-Olkin family of distribution (CMO). Graphical, numerical and analytical approach was explored to study the properties and applicability of the new CMO family of distribution. Special representations and important reliability properties and other statistical properties were defined. Simulation study was conducted in order to have an insight on the estimates of the three parameters model using maximum products of spacing (MPS). Emphases on the greater flexibility of the new CMO family of distribution beyond the cosine-G family and other top models of the Cosine related family was made through Weibull distribution. The results revealed the superiority of the Cosine Marshall-Olkin Weibull model (CMO-W) over others via two data sets. [ABSTRACT FROM AUTHOR]