Chebyshev polynomials are a sequence of orthogonal polynomials that arise in various areas of mathematics, particularly in approximation theory. They are defined on the interval [-1, 1] and are denoted as T_n(x), where n indicates the degree of the polynomial. These polynomials are useful for minimizing the error in polynomial interpolation and are closely related to the cosine function. There are two main types of Chebyshev polynomials: the first kind, T_n(x), and the second kind, U_n(x). The first kind is defined using the cosine function, while the second kind is related to the sine function. Both types exhibit important properties, such as extremal behavior and oscillation, making them valuable in numerical analysis and engineering applications.