Maclaurin series enables the approximation of functions as a sum of terms involving derivatives at a specific point. For the sine function, starting at x = 0, it takes the form: sin(x) ≈ x – x³/3! + x^5/5! – x^7/7! + …. This series is derived using Taylor’s theorem, which provides a systematic method for approximating functions using power series. Maclaurin series has wide applications in calculus, physics, and engineering, where accurate approximations are crucial.