Use the Alternating Series Estimation Theorem or Taylor's Inequality to Estimate

Short Answer

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of $x$ for which the given approximation is accurate to within the stated error.
$\cos x \approx 1 - \frac { x ^ { 2 } } { 2 } + \frac { x ^ { 4 } } { 24 } \quad \mid$ error $\mid < 0.08$
Write $a$ such that $- a < x < a$ .