Let $T _ 5 (x)$ be the fifth degree Taylor polynomial of $\cos\!\left(0.3x\right)$ centered at $0.$

a. Find $T_5(x).$ (Enter a function. Don't use factorials in your answer.)

$T_{5} (x) =$

b. Find the largest integer $k$ such that if $\vert x \vert < 1,$ the Taylor polynomial $T_{5}(x)$ approximates $\cos\!\left(0.3x\right)$ with error less than $10^{-k}.$

$k =$