In this article, we propose and study an improved version of the cosine distribution. Its main features are to be with support [-1, 1], to be mainly asymmetric by construction, and to be simple and flexible from a functional point of view, in particular, it retains the cosine feature that allows it to generate oscillatory shapes and multimodes, to unify the cosine distribution and the truncated exponential distribution, and to be used as a statistical model in different scenarios involving data contained in [-1, 1]. We provide the main theory, including an expression of the key functions, quantiles and moments. Numerical work is carried out to determine the main measures of skewness and kurtosis. The practicality of the proposed distribution is illustrated with some data fitting scenarios, supported by graphical analysis.