Problem: Use the Lagrange interpolating polynomial of degree three or less and four digit chopping arithmetic to approximate cos(.750) using the following values. Find an error bound for the approximation.
cos(.6980) = 0.7661 cos(.7330) = 0.7432 cos(.7680) = 0.7193 cos(.8030) = 0.6946
The actual value of cos(.7500) = 0.7317 (to four decimal places). Explain the discrepancy between the actual error and the error bound.
Solution: The approximation of cos(.7500) 0.7313. The actual error is 0.0004, and an error bound is 2.7 × 10^(-8). The discrepancy is due to the fact that the data are given only to four decimal places.
Can anyone help me figure out the intermediary steps from the problem to solution?