Maclaurin formula: finding a delta for a given error

Approximate the function $f(x)=\sin(x)$ using the corresponding Maclaurin polynomial: $P_5(x)$, in a bound $\epsilon(0,\delta)$. Determine a value of $\delta>0$, so that the rest $R_5(x)$ verifies $|R_5(x)|<0.0005$ for all $x\in{\epsilon(0,\delta)}$

Well, the first thing that puzzles me a bit is that the order for $P_5$ and $R_5$ is the same. I assume that it is a mistake, and that the polynomial must be $P_4$, or the rest $R_6$. I have chosen to leave the degree of the polynomial as it was and turn up one grade to the rest.

So I have to find a delta for which any value within the environment $(0,\delta)$ is less than the error 0.0005

So I did:

$R_6(x)=|\displaystyle\frac{\sin(\alpha)x^6}{6!}|<0 .0005$ $0<\alpha

So I must find x:

$R_6(x)=|\sin(\alpha)x^6|<0.36$ $0<\alpha

I must find x that satisfies the equation: $\sin(x)x^6<0.36$

I don't know how to go ahead.

Bye there.