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

\fill[lightgray] (-3,-3)--(3,-3)--(-3,3);
\draw[thin,->] (-3,0) -- (9,0) node[above]{$x$};
\draw [thin,->] (0,-3) -- (0,3) node[right]{$t$};

\draw[thick] (3,-3) --(-3,3);
\draw[blue] (0,0) -- (9,3);
\draw[teal] (0,0) -- (9,-3);
\node at (5,0) {\colorbox{yellow}{$u= -\cos(x+3t) +5\cos (x-3t)$}};
\node at (2,2.5) {\colorbox{yellow}{$u = -\cos(x+3t) -2\cos ((x-3t)/2) +7$}};
\node at (2.5,-2.5) {\colorbox{yellow}{$u= \frac{5}{2}\cos(2x+6)-\frac{7}{2} + 5\cos(x-3t)$}};

\end{tikzpicture}
\end{document}