Question

What is the exact value of arccos(−2√2) ?

Answer 1

Answer:

See explanation

Step-by-step explanation:

The range of the cosine function is $-1\le \cos x\le 1$

Therefore $arc \cos (-2\sqrt{2})$ is not defined.

Assuming your question is rather $arc \cos (-\frac{\sqrt{2}}{2})$

Then $arc \cos (-\frac{\sqrt{2}}{2})=\pi-arc \cos (\frac{\sqrt{2}}{2})$  in the second quadrant.

$arc \cos (-\frac{\sqrt{2}}{2})=\pi-\frac{\pi}{4}$

$arc \cos (-\frac{\sqrt{2}}{2})=\frac{3\pi}{4}$