I actually already have the solution to this, but would just like some clarification of how the solution was reached.
The solutions provided used the fact that by Taylor's theorem,
$\sin x = T_6(x) + R_6(x) $
The rest of the solution I understand, but how do you know to use the 6th degree Taylor polynomial? Why not 5th or 7th?
Any explanation would be greatly appreciated! Thanks so much!