algebra precalculus - If we know $sin alpha$ and $cos alpha.$ can we find the angle $alpha$?

For example
$$\sin \alpha=\frac{8}{\sqrt{65}}, \cos \alpha=\frac{1}{\sqrt{65}}$$

Can we analytically find $\alpha$ ? The only thing I did was calculate $\tan$; it isn't helpful.

It turns out my question is if we know $\cos \alpha $ and $\sin \alpha$ is there a formula for $\arcsin$ and $\arccos$ ? The only way of finding arcsin or arccos that i know is using a calculator