Chapter 4, Problem 2P

The Maclaurin series expansion for cos x is

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

Starting with the simplest version, $\cos x=1$, add terms one at a time to estimate $\cos \left(\pi /3\right)$. 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.