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

$sinxsinx-\frac{x^3}{3x}\frac{x^3}{2y}$

when $-0\mathrm{.}3x0\mathrm{.}37.$ Use this approximation to find sin$(12\text{'})$ correct to stex decimal places.

$($b$)$ Bor what yolues of $x$ is this spprodimation sccurate to sitlin $0\mathrm{.}0005?$