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These basis functions are employed to construct B\u00e9zier\u2010like curves, termed \u201ctrigo\u2010curves\u201d, which retain the fundamental properties of classical B\u00e9zier curves while offering enhanced shape control through parameter adjustment, independent of control point positions. We establish the monotonicity\u2010preserving nature of these curves. Additionally, we develop a new class of linear positive operators based on these trigonometric basis functions. The operators, incorporating an auxiliary parameter, are thoroughly analyzed for their fundamental properties. We establish their convergence rate, derive a modified Voronovskaja theorem, and obtain error bounds in terms of the modulus of continuity. 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