Find the domain of the vector-valued function.
$$\begin{aligned}
&\mathbf{r}(t)=\mathbf{F}(t)+\mathbf{G}(t), \text { where }\\
&\mathbf{F}(t)=\cos t \mathbf{i}-\sin t \mathbf{j}+\sqrt{t} \mathbf{k}, \quad \mathbf{G}(t)=\cos t \mathbf{i}+\sin t \mathbf{j}
\end{aligned}$$