Using Matlab:

Use an appropriate Taylor series to write a MATLAB function M$-$file that approximates $f(x)=$

$sin(x)$ for all $x$ with a maximum error of ${10}^{-15}.$ That is$,$ your M$-$file should take values of $x$ as

input, return values of $sinx$ as output, but should not use MATLAB's built$-$in function sin$.$m$.$

Hint: You might find MATLAB's built$-$in file mod useful in dealing with the periodicity.