# How do you find lim sintheta as theta->oo?

$\sin \left(\theta\right)$ oscillates in between $- 1$ and $1$ as $\theta$ approaches $\infty$. In other words, it does not converge to a single value.
One way to show this is through the definition of a limit to positive infinity, which states that, if ${\lim}_{x \to \infty} f \left(x\right) = L$, then for any given $\epsilon > 0$, however small, there exists some $c$ such that $L - \epsilon \le f \left(x\right) \le L + \epsilon$ for all $x > c$.
This is clearly impossible for ${\lim}_{\theta \to \infty} \sin \left(\theta\right)$, as no matter how large $\theta$ is, $\sin \left(\theta\right)$ will still oscillate between $- 1$ and $1$. Thus, the limit does not exist.