Question

2. Given the table \begin{tabular}{c|ccccc} $x$ & 0 & $\frac{\pi}{6}$ & $\frac{\pi}{4}$ & $\frac{\pi}{3}$ & $\frac{\pi}{2}$ \\ $\cos x$ & 1 & $\frac{\sqrt{3}}{2}$ & $\frac{1}{\sqrt{2}}$ & $\frac{1}{2}$ & 0 \\ \end{tabular} construct a fourth order interpolating polynomial for $\cos x$ and use it to approximate $\cos(\frac{\pi}{7})$ and find a bound on the error. You can use any method you wish to compute the interpolating polynomial, but you must explain what you did in any case.

          2. Given the table
\begin{tabular}{c|ccccc}
$x$ & 0 & $\frac{\pi}{6}$ & $\frac{\pi}{4}$ & $\frac{\pi}{3}$ & $\frac{\pi}{2}$ \\
$\cos x$ & 1 & $\frac{\sqrt{3}}{2}$ & $\frac{1}{\sqrt{2}}$ & $\frac{1}{2}$ & 0 \\
\end{tabular}
construct a fourth order interpolating polynomial for $\cos x$ and use it to approximate $\cos(\frac{\pi}{7})$ and find a bound on the error. You can use any method you wish to compute the interpolating polynomial, but you must explain what you did in any case.

2. Given the table

x 0 (π)/(6) (π)/(4) (π)/(3) (π)/(2)

cos x 1 (√(3))/(2) (1)/(√(2)) (1)/(2) 0

construct a fourth order interpolating polynomial for cos x and use it to approximate cos((π)/(7)) and find a bound on the error. You can use any method you wish to compute the interpolating polynomial, but you must explain what you did in any case.

Added by Michael H.

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