$($a$)$ What is the maximum error possible in using the approximation

$sinx$~~$x-\frac{3^3}{3!}\frac{x^5}{5!}$

when $-0\mathrm{.}3x0\mathrm{.}3?$ Use this approximation to find $sin(12)$ correct to six decim places.

$($b$)$ For what values of $x$ is this approximation aceurate to within $0\mathrm{.}00005?$