How to solve $ \sqrt 2 \cos 2x = -1$? I have this equation,   $ \sqrt{2} \cos 2x = -1$. I need all solutions between $[0,2\pi]$. I simplified that to $\cos 2x = -\frac{1}{\sqrt{2}}$.
I could just use a calculator and do $\arccos{-\frac{1}{\sqrt{2}}}$, to get angles for $2x$, but I need it in terms of $\pi$, and I also feel like I'm missing something simple that will allow me to find the solutions without one.
Should I just do it with a calculator? Or am I missing something here?
Thanks!

$$\cos (2x) = -\frac 1{\sqrt 2} \iff 2x = \arccos \left(-\frac{1}{\sqrt 2}\right)\iff x = \frac 12 \arccos  \left(-\frac{1}{\sqrt 2}\right)$$ 
You'll find, then, that $$x=3\pi/8, \;5\pi/8,\; 11\pi/8,\; 13\pi/8$$
