I am beginning trigonometric limits. I believe this limit requires a substitution but I am not quite sure exactly how the substitution works. Any explanations on the process of this specific question would be wonderful. Given:
$$\lim_{x \to \pi} \dfrac{\sin x}{\pi-x}$$
I need to determine the limit. I think I have to rewrite the limit approaching part and I am guessing this will involve the following:
$$\lim_{x \to 0} \dfrac{\sin x}{x}=1$$
Note: my course so far has not covered L'hospitals rule.
Thanks