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. The first few Chebyshev Polynomials are T_0(x) = 1, T_1(x) = x, and T_2(x) = 2x² - 1. They exhibit important properties, such as oscillating between -1 and 1, and their roots are evenly spaced in the interval. Chebyshev Polynomials are widely used in numerical methods, including Chebyshev approximation and spectral methods.