M S $1.($a$)$ Implement the function plot$\_$sint on your computer, and use it to compare different degrees of approximation on the intervals $0,1$

$0,2$

$0,3,$ and $0,4.$ Comment as best as you can on the accuracy of the approximations.

$($b$)$ Modify the program by allowing for larger degrees of approximation, for example, in the program use

degree $=[4,8,12,16]$

Repeat part $($a$)$ and also consider longer intervals $0,b.$