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

To evaluate the limit \( \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi) \), we can start by substituting \( x \) with \( 3\pi \): \[ \sin(x - 3\pi) = \sin(3\pi - 3\pi) = \sin(0) \] Since \( \sin(0) = 0 \), we have: \[ \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi) = 0 \] Thus, the exact answer is: \[ \lim _{x \rightarrow 3 \pi} \sin (x-3 \pi) = 0 \]