Answer
The domain $D$ resides between the lines $x+y=-1$ and $x+y=1$:
$D = \left\{ {\left( {x,y} \right)| - 1 \le x + y \le 1} \right\}$
Work Step by Step
Let $\theta = {\cos ^{ - 1}}\left( {x + y} \right)$. Since $ - 1 \le \cos \theta \le 1$, so $ - 1 \le x + y \le 1$. Thus, the domain $D$ resides between the lines $x+y=-1$ and $x+y=1$:
$D = \left\{ {\left( {x,y} \right)| - 1 \le x + y \le 1} \right\}$
