8. Recall that we can define an inner product on the set PC[a, b] as follows: (f.g) = ["f f(x)g(x) dx and we can define a norm on the same set as: ||f|| = √(f. f) a. Show that the functions f(x) = x and g(x) = cos (x) are orthogonal in the set PC[-π, π]. b. Compute the norm |cos (x) || in the set PC[-, π].

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