Yup, we chose coefficients that can't even be represented in our number system. Of course the results have error. As for what we can do about it, notice where the error occurs. It only becomes excessive as Equation x approaches Equation plus-or-minus pi , at which point Equation ModifyingAbove sine With caret left-parenthesis x right-parenthesis should approach 0. But the slight bit of error in the coefficients makes it so it doesn't approach 0 at quite the right place. Our polynomial already has a factor of Equation x explicitly factored in order to create a root at Equation x equals 0 . My instincts are to pull out a factor of Equation left-parenthesis x minus pi right-parenthesis and Equation left-parenthesis x plus pi right-parenthesis as well.