This problem uses the 'for' command.

The sine of xCreate an m$-$function file that takes x $(0$ x $$ pi$/4)$ and n $($a natural number$)$ as inputs and calculates the value of sin$($x$)$ up to the $(2$n$-1)$th polynomial. If the function name is mysine, then the filename of this function will be mysine.m$.$ Use MATLAB's built$-$in factorial$($n$)$ function to obtain the factorials used in the series expansion.

Fill in the table below and submit it $($execute 'format long' in the command window to display $15$ significant digits$).$ can be expressed

using a series expansion as follows.

mysine$($pi$/16,5)->$ ans $=0\mathrm{.}195090322016129$

mysine$($pi$/16,3)->$ ans $=0\mathrm{.}195090324247368$

mysine$($pi$/16,1)->$ ans $=0\mathrm{.}196349540849362$