Chebyshev polynomials of the first kind are a sequence of orthogonal polynomials defined on the interval [-1, 1]. They are denoted as T_n(x), where n is a non-negative integer. These polynomials can be expressed using the cosine function: T_n(x) = cos(n * arccos(x)). They play a significant role in approximation theory and numerical analysis. These polynomials exhibit several important properties, including extremal behavior and minimization of the maximum error in polynomial interpolation. They are widely used in various fields, such as signal processing, computer graphics, and numerical methods, due to their efficiency in approximating functions.