Problem $-04$: $,$ Write a MATLAB function $($M$-$file$)$ to compute the Maclaurin series expansion

for the sine function as outlined below.

$sin(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}-\frac{x^7}{7!}+\frac{x^9}{9!}-$dots

function $[si{n}_{e}st,e_a,nu{m}_t$erms$]=maclauri{n}_{sine(x,e_{-}s,t_{-}\text{m}\text{a}\text{x})}$

The function should include the following features:

Allow the user to input values for x $,$ e$\_$s$,$ and an optional parameter for t$\_$max $($otherwise default to

$.$

Iterate until the approximate error falls below a specified stopping criterion $($e$\_$s$)$ or until the maximum

number of terms $($t$\_$max$)$ is reached.

The function should return the estimated value of $sin(x),$ the absolute approximate error, and the

number of terms used.