Chapter 3.2, Problem 8E

Use the Lagrange interpolating polynomial of degree 3 or less and four-digit chopping arithmetic to approximate cos 0.750 using the following values. Find an error bound for the approximation. $\begin{array}{ll}\cos 0.698=0.7661\hfill & \cos 0.733=0.7432\hfill \\ \cos 0.768=0.7193\hfill & \cos 0.803=0.6946\hfill \end{array}$

The actual value of $\cos 0.750$ is 0.7317 (to four decimal places). Explain the discrepancy between the actual error and the error bound.