Evaluate \( \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi) \) Enter the exact answer. \( \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi)= \) Number

1. The limit is given by \[ \lim_{x \rightarrow 3\pi} \sin (x-3\pi) \] 2. Notice that as \( x \rightarrow 3\pi \), the expression \( x-3\pi \) approaches 0: \[ \lim_{x \rightarrow 3\pi} (x-3\pi) = 0 \] 3. Substitute this result into the sine function: \[ \sin (x-3\pi) \rightarrow \sin(0) \] 4. Since \(\sin(0) = 0\), we conclude that: \[ \lim_{x \rightarrow 3\pi} \sin (x-3\pi) = 0 \] 5. Therefore, the exact answer is \(0\).