Answer
The domain: $D = \left\{ {\left( {r,s} \right)| - 1 \le rs \le 1} \right\}$
The range is the interval $\left[ {0,\pi } \right]$.
Work Step by Step
Let $\theta = {\cos ^{ - 1}}\left( {rs} \right)$. Since $ - 1 \le \cos \theta \le 1$, so $ - 1 \le rs \le 1$. Thus, the domain resides between the curves $s = - \frac{1}{r}$ and $s = \frac{1}{r}$ for $r \ne 0$ and $s \ne 0$. The domain can be described by the set
$D = \left\{ {\left( {r,s} \right)| - 1 \le rs \le 1} \right\}$
The range of $g\left( {r,s} \right)$ is the range of the inverse cosine, that is, the interval $\left[ {0,\pi } \right]$.
