Write a python program for Hermite Interpolation, name this function as $$Hermite$.($Please refer to Algorithm $3\mathrm{.}3$ on lecture note$)$ Then use this function to solve the following question. $1.$ Use the following values and five$-$digit rounding arithmetic to construct the Hermite interpolating polynomial to approximate sin $0\mathrm{.}34.$ x $($radians$)$ sin x Dx sin x $=$ cos x $0\mathrm{.}300\mathrm{.}295520\mathrm{.}955340\mathrm{.}320\mathrm{.}314570\mathrm{.}949240\mathrm{.}350\mathrm{.}342900\mathrm{.}93937$