Although I know a couple of proofs of the statement $$ \lim_{x \to 0 } \frac{\sin x}{x} = 1, $$ I would like to be able to come up with a proof using the definition of the limit (i.e. an $\epsilon$-$\delta$ proof). Here $x$ is in radians of course.
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No matter what your path to a proof, you will always need to use some specific property of the sine function, as most textbooks do. – Lubin Mar 15 '14 at 21:43