## University Calculus: Early Transcendentals (3rd Edition)

$\lt 0.0026$
The Taylor series for $\cos x$ can be defined as: $\cos x=1-\dfrac{x^2}{2}+\dfrac{ x^3}{3}-....$ Since, the term $1-\dfrac{x^2}{2}$ is too small by the Alternating Series Estimation Theorem. So, the error is less than $\dfrac{(0.5)^4}{24} \lt 0.0026$ by the Alternating Series Estimation Theorem.