Determine the number of terms necessary to approximate $cosx$ to $8$ significant figures using

Maclaurin series approximation.

$cosx=1-\frac{x^2}{2}+\frac{x^4}{4!}-\frac{x^6}{6!}+\frac{x^8}{8!}-$cdots

Calculate and display the approximation using a value of $x=0\mathrm{.}3.$

a$.$ Do this by hand using $4$ terms to evaluate $cosx.$ Compute relative true error $(\%)$ and

relative approximate error $(\%)$ as terms are added. Create a table that shows the

iteration number, calculated value of $cosx,$ relative true error $($that you can

calculate based on the built$-$in cosine function in your calculator or Excel$)$ and

relative approximate error.

b$.$ Write a Matlab function to evaluate the series. The code should allow an infinite

number of terms, but should be used to evaluate the series to $8$ significant figures.

The code should also be able to run until it reaches either a maximum number of

iterations $($specified by the user$)$ or a stopping criterion $($such as a minimum relative

approximate error, specified by the user in $\%).$ Include default values of maxit

$(=100)$ in the event that they are not specified by the user. Output a table that

shows the iteration number, calculated value of $cosx,$ relative true error $($that you

can calculate based on the built$-$in cosine function$)$ and relative approximate error.