Use the Lagrange interpolating polynomial of degree three or less and four-digit chopping arithmetic to approximate cos 0.750 using the following values. Find an error bound for the approximation.
cos 0.698 = 0.7661 cos 0.733 = 0.7432 cos 0.768 = 0.7193 cos 0.803 = 0.6946
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.