Conditional line style when plotting curve with PGFPlots

Question

I want to plot a function with different styles according to the domain. For example:

\documentclass[tikz]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        scale only axis=true,
        height=2.8cm,
        width=16cm,
        axis lines=middle,
        xmin=-11,
        xmax=11,
        ymax=1.15,
        ymin=-1.15,
        xtick={-3*pi,-2*pi,-pi,pi,2*pi,3*pi},
        xticklabels={$-3\pi$,$-2\pi$,$-\pi$,$\pi$,$2\pi$,$3\pi$},
        ytick distance=1,
        legend style={
            at={(0.5,1.14)},
            anchor=south,
            legend columns=-1
        },
    ]
        \addplot[domain=-pi/2:pi/2,samples=50,red] {sin(deg(x))};
        \addplot[domain=-3*pi:-pi/2,samples=50,red,dashed] {sin(deg(x))};
        \addplot[domain=pi/2:3*pi,samples=50,red,dashed] {sin(deg(x))};
        \addplot[domain=0:pi,samples=50,blue] {cos(deg(x))};
        \addplot[domain=-3*pi:0,samples=50,blue,dashed] {cos(deg(x))};
        \addplot[domain=pi/2:3*pi,samples=50,blue,dashed] {cos(deg(x))};
    \end{axis}
\end{tikzpicture}


\end{document}

This plots both the sine and the cosine, with a solid line in certain domains, and dashed elsewhere. Is there a way to do this in a single command with PGFPlots? There are certainly ways to do it with 'pure' TikZ, but I want to accomplish this specifically with PGFPlots. Thanks!