\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}

\fill[lightgray] (1,-1)--(-6,-1)--(-6,6);
\draw[thin,->] (-6,0) -- (6,0) node[above]{$x$};
\draw [thin,->] (0,-1) -- (0,6) node[right]{$t$};

\draw[thick] (1,-1) --(-6,6);
\draw[blue] (0,0) -- (2,6);
\draw[teal] (0,0) -- (-2,6);
\node at (3,0) {\colorbox{yellow}{$u=\sin(3x+t) +3\sin (3x-t)$}};

\node at (0,5) {\colorbox{yellow}{$u=\sin(3x+t)$}};

\node at (-3,5) {\colorbox{yellow}{$u=0$}};
\end{tikzpicture}
\end{document}