DE algorithm is one of the most popular and powerful evolutionary algorithms for global optimization problems. However, the performance of DE is greatly influenced by the selected suitable mutation strategy and parameter settings, but this choosing task is a challenge work and time-consuming. In order to solve this defect, a novel bare-bones differential evolution algorithm based on trigonometry, called tBBDE, is proposed in this paper. The convergence performance of the algorithm is then analyzed in terms of the stochastic functional theory. In the paper the proposed algorithm adopts the triangle Gaussian mutation strategy as well as ternary crossover and adaptive crossover probability strategy for individual update. When the algorithm is trapped into premature convergence and stagnation, it will execute population disturbance. In this case, the proposed algorithm not only inherits the advantages of bare-bones algorithm but also retains the characteristics of DE evolution based on the differential information of randomly selected individuals. The experimental studies have been conducted on 26 benchmark functions including unimodal, multimodal, shifted and high-dimensional test functions, while the results have verified the effectiveness and reliability. Besides, comparied with the other bare-bones algorithms and the state-of-the-art, DE variants has proved that the algorithm is a type of new competitive algorithm.