Okay, so I have the function,

$\displaystyle \cos x = -\frac{1}{\sqrt{2}}$ for $\displaystyle -\pi \le x \le \pi$

Basic angle $\displaystyle = \cos^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi}{4}$

$\displaystyle \cos$ is negative in 2nd + 3rd quadrants

$\displaystyle x= \cos^{-1}\left(\frac{1}{\sqrt{2}}\right)$

$\displaystyle x= \pi-\frac{\pi}{4}, \pi + \frac{\pi}{4}$

$\displaystyle x= \frac{3\pi}{4}, \frac{5\pi}{4}$

$\displaystyle \frac{3\pi}{4}$ is one solution. However $\displaystyle \frac{5\pi}{4}$ is not in the domain so I assume it it not a solution?

The book tells me there is another solution $\displaystyle = -\frac{3\pi}{4}$

How do I obtain this solution?

It is confusing when going in a clockwise direction of the unit circle.

Thanks.