Chapter 5.5, Problem 303E

The following series do not satisfy the hypotheses of the alternating series test as stated.

In each case, state which hypothesis is not satisfied. State whether the series converges absolutely.

303. How many terms in $\cos \theta =1-\frac{{\theta }^2}{2!}+\frac{{\theta }^4}{4!}+\frac{{\theta }^6}{6!}+\mathrm{...}$ are needed to

approximate cos 1 accurate to an error of at most

0.00001?