Suppose we want to use the Chebyshev interpolation to approximate f(x) = sin(x) on the interval [0, 1] with n= 2 (i.e., 3 interpolation points). (a) Find the Chebyshev nodes on [0, 1]. (b) Find the second degree polynomial q(x) that interpolates f(x) at the Chebyshev nodes. (c) Estimate the error bound of q(x) on the interval [0, 1]. Compare the error bound with the one obtained in 1(b); which is more accurate?

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