If $\theta =\frac{-11\pi }{6}$, then
$$\sin (\theta )=$$
$$\cos (\theta )=$$

Step 1 ：The given angle is $\theta =\frac{-11\pi }{6}$.

Step 2 ：The sine and cosine functions are periodic with a period of $2\pi$. This means that $\sin (\theta +2\pi )=\sin (\theta )$ and $\cos (\theta +2\pi )=\cos (\theta )$ for any real number $\theta$.

Step 3 ：So, if $\theta =\frac{-11\pi }{6}$, we can add $2\pi$ to $\theta$ until we get a number in the range $[0,2\pi )$. This will not change the values of $\sin (\theta )$ and $\cos (\theta )$.

Step 4 ：The equivalent angle in the range $[0,2\pi )$ is $\theta =0.524$ (rounded to three decimal places).

Step 5 ：The sine of this angle is $\sin (\theta )=0.500$ (rounded to three decimal places) and the cosine of this angle is $\cos (\theta )=0.866$ (rounded to three decimal places).

Step 6 ：Therefore, we have: $\sin \left(\frac{-11\pi }{6}\right)=\boxed{{\displaystyle 0.500}}$ and $\cos \left(\frac{-11\pi }{6}\right)=\boxed{{\displaystyle 0.866}}$.