Answer
$cosx=\Sigma_{n=0}^{\infty}(-1)^{n+1}\frac{(x-\pi)^{2n}}{(2n)!}$
The radius of convergence is $R=\infty$.
Work Step by Step
Taylor series centered at $a= \pi$ is
$-1+\frac{1}{2!}(x-\pi)^{2}-\frac{1}{4!}(x-\pi)^{4}+....$
$cosx=\Sigma_{n=0}^{\infty}(-1)^{n+1}\frac{(x-\pi)^{2n}}{(2n)!}$
The radius of convergence is $R=\infty$.
