$($a$)$ Find the approximations $T_{10},M_{10},$ and $S_{10}$ for ${\displaystyle \underset{0}{\overset{}{}}}16sin(x)dx.($Round your answers to six decimal places.$)$

$T_{10}=$

$M_{10}=$

$S_{10}=$

Find the corresponding errors $E_T,E_M,$ and $E_S.($Round your answers to six decimal places.$)$

$E_T=$

$E_M=$

$E_S=$