Chapter 6, Problem 23P

The Taylor series expansion for cos(x) is:

$\cos \left(x\right)=1-\frac{x^2}{2!}+\frac{x^4}{4!}-\frac{x^6}{6!}+\mathrm{...}={\displaystyle \underset{n=0}{\overset{\infty }{\sum }}\frac{{\left(-1\right)}^n}{\left(2n\right)!}}{x}^{2n}$

wherex is in radians. Write a MATLAB program that determines cos(x) using the Taylor series expansion. The program asks the user to type a value for an angle in degrees. Then the program uses a loop for adding the terms of the Taylor series. If a_nis the nth term in the series, then the sum S_nof the n terms is $S_n=S_{n-1}+a_n$ . In each pass calculate the estimated error E given by $E=\left|\frac{S_n-S_{n-1}}{S_{n-1}}\right|$ . Stop adding terms when $E\le 0.000001$ . The program displays the value of cos(x). Use the program for calculating:

1. Cos(35°)
2. sin(125°)

Compare the values with those obtained by using a calculator.