1. Consider the function f(x) = cos(x). Solve the Gauss approximation problem min\f(x) = p(x)² dx, where P2 denotes the set of polynomials of degree <2. You may use that the functions 90(x) = 2πT 3 x 91(x) = 2п п 92(x) = 357 (³ (2)² - 1) form an orthonormal basis of P2 with respect to the L2-scalar product on the interval [-T, π]. Find an explicit expression for p(x) and sketch (plot) your results for p and the cosine function on the interval [-π,π].

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