Limits as x approaches 0

Question

I was wondering how this worked when submitted, anything over 0 was infinite.

Answer 1

well, $$ \cos( \frac{\pi}{2} - x ) = \sin( \frac{\pi}{2} - \frac{\pi}{2} + x ) = \sin x $$.

Hence,

$$ \frac{ \sin x}{x} \to_{x \to 0 } 1 $$