1. Consider interpolating the function f(x) = sin(x) at the interpolation points To = 0, X1 = 1/2, 12 = 1. (a) Give the three Lagrange basis polynomials corresponding to these three interpo- lation points. (b) Give the three Newton basis polynomials corresponding to these three interpola- tion points. (c) Using either the Lagrange or Newton basis polynomials, give the quadratic func- tion that interpolates f(r) = sin(r) at the three interpolation points given