Answer
$\lt 0.0026$
Work Step by Step
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.
