Problem $1[20$ marks$].$ Suppose you need to implement a routine to compute the stan$-$

dard trigonometric function cos$($x$)$ on an embedded microprocessor that does not have a

built$-$in trigonometric function. You are require to develop a MATLAB function that com$-$

putes cos$($x$)$ without using the built$-$in cos$($x$)$ function. Your routine should use only basic

arithmetic operations, including multiplies, divides, additions and subtractions.

a$.[8$ marks$]$ Develop a function for cos$($x$)$ in MATLAB and optimize your code. Addi$-$

tionally, ensure to include comments as necessary for clarity and understanding.

b$.[8$ marks$]$ Examine three distinct accuracy levels to evaluate their influence on the ac$-$

curacy of your computations. Plot absolute errors against x values, within the interval

$[2\backslash$pi $,3\backslash$pi $].$ Provide insights derived from the obtained results.

c$.[4$ marks$]$ Analyze the relationship between average absolute error and the order of

accuracy. Provide insights derived from the obtained results.