Question

How do you evaluate `arccos(-1/sqrt2)`?

Answer 1

As the range is not specified, the general value is given. The principal value of `arc cos(-1/sqrt2)` is `(3pi)/4`.
The general value is `2kpi+-(3pi)/4`, k = 0. 1. 2. 3.,...

Explanation:

Cosine is positive in the 1st quadrant [0, pi/2] and negative in the second `[pi/2, pi]`

The principal value for arc cos is defined to be in `[0, pi]`.

The general value is `2kpi+-`(principal value), k = 0. 1. 2. 3.,...

Here, the principal value of `arc cos (-1/sqrt2) = (3pi)/4`.