1. The problem asks for the limiting value of the function $$f(x) = \sin x$$ as $$x$$ approaches $$\pi$$. 2. The limit of a function $$f(x)$$ as $$x$$ approaches a value $$a$$ is the value that $$f(x)$$ gets closer to as $$x$$ gets closer to $$a$$. 3. We use the fact that $$\sin x$$ is continuous everywhere, so $$\lim_{x \to a} \sin x = \sin a$$. 4. Therefore, $$\lim_{x \to \pi} \sin x = \sin \pi$$. 5. We know from the unit circle that $$\sin \pi = 0$$. 6. Hence, the limiting value of $$\sin x$$ as $$x$$ approaches $$\pi$$ is $$0$$. Final answer: C $$0$$