5. (20 pts) (Problem 4.1) The Maclaurin series expansion (a Maclaurin series is a Taylor series expansion of a function about 0) for cos x is \cos x=1-\frac{x^{2}}{2}+\frac{x^{4}}{4 !}-\frac{x^{6}}{6 !}+\frac{x^{8}}{8

!}-\cdots (a) Starting with the simplest version, cos x = 1, add terms one at a time to estimate cos(t/3). After each new term is added, compute the true and approximate percent relative errors. Use your pocket calculator to determine the true value. Add terms until the absolute value of the approximate error estimate falls below an error criterion conforming to two significant figures. Show the steps and make a table to show your results. (b) Write a function using this Maclaurin series in MATLAB to calculate cos(7/6), cos(T/2), and cos(5a/6). Plot a curve of cos x.