Rewrite $\sin \left(x+\frac{11 \pi}{6}\right)$ in terms of $\sin x$ and $\cos x$. Simplify your answer Enclose arguments of functions in parentheses. For example, sin $(2 x)$ \[ \sin \left(x+\frac{11 \pi}{6}\right)= \]

Step 1 ：Rewrite \(\sin \left(x+\frac{11 \pi}{6}\right)\) in terms of \(\sin x\) and \(\cos x\) using the angle sum formula for sine: \(\sin(a + b) = \sin a \cos b + \cos a \sin b\)

Step 2 ：Let \(a = x\) and \(b = \frac{11 \pi}{6}\)

Step 3 ：Find the values of \(\sin \frac{11 \pi}{6}\) and \(\cos \frac{11 \pi}{6}\): \(\sin \frac{11 \pi}{6} = -0.5\) and \(\cos \frac{11 \pi}{6} = 0.866\)

Step 4 ：Substitute the values into the angle sum formula: \(\sin \left(x+\frac{11 \pi}{6}\right) = \sin x \cos \frac{11 \pi}{6} + \cos x \sin \frac{11 \pi}{6}\)

Step 5 ：\(\sin \left(x+\frac{11 \pi}{6}\right) = 0.866 \sin x - 0.5 \cos x\)

Step 6 ：\(\boxed{\sin \left(x+\frac{11 \pi}{6}\right) = 0.866 \sin x - 0.5 \cos x}\)