Answer
$(-\infty,\infty)$
Work Step by Step
Both trigonometric functions and polynomials have as their domain all real numbers. Thus, the domains of the $\textbf{i}$, $\textbf{j}$, and $\textbf{k}$ components are all $(-\infty,\infty)$, so their intersection is $(-\infty,\infty)$.