# Sequence of sin(1/n) Why does it not converge

$\lim_{n\rightarrow \infty} a_{n} = \sin(\frac{1}{n}) = \sin(\frac{1}{\infty}) = sin(0) = 0$ Converges to Zero
$\lim_{n\rightarrow \infty} a_{n} = \sin(\frac{1}{n}) = \sin(\frac{1}{\infty}) = sin(0) = 1?$