I am asked find the following limit
$\lim_{\theta \rightarrow 0}\frac {\sin^2\theta}{\theta}$
I recognize that $\lim_{\theta \rightarrow 0}\frac{\sin\theta}{\theta}=1$
But because I have $sin^2\theta$ in the numerator, I am left with...
$\lim_{\theta \rightarrow 0}1(\sin\theta)$
When I think about what this implies, I reason that the ratio of the opposite side over hypotenuse of the angle $\theta$ must approach approach zero, but for this to happen the opposite side would have a value of zero, which means the triangle formed would have no x component.
$\lim_{\theta \rightarrow 0}1(\sin\theta)=0$
Is my reasoning correct? Am I thinking about this question in a constructive manner?