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\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
vardef pi_sixths(expr n) =
save s, f, q; string s, f; numeric q;
s = if n < 0: "-" else: "" fi; q = abs(n);
if q mod 6 = 0:
f = if q > 6: decimal 1/6 q else: "" fi;
elseif q mod 3 = 0:
f = "\frac{" & decimal 1/3 q & "}{2}";
elseif q mod 2 = 0:
f = "\frac{" & decimal 1/2 q & "}{3}";
else:
f = "\frac{" & decimal q & "}{6}";
fi
"$\scriptstyle" & s & f & "\pi$"
enddef;
beginfig(1);
numeric u, pi; u = 50; pi = 3.141592653589793;
path xx, yy;
xx = (3.5 left -- 4 right) scaled u;
yy = (1.2 down -- 1.3 up) scaled u;
path ss, tt, uu;
ss = origin for x=1 upto 360: -- (x, sind(x)) endfor;
tt = origin for x=1 upto 360: -- (x, 1/2 sind(3x)) endfor;
uu = origin for x=1 upto 360: -- (x, ypart point x of ss + ypart point x of tt) endfor;
forsuffixes $=ss, tt, uu:
$ := $ shifted 360 left & $;
$ := $ xscaled (pi/180) scaled u;
$ := $ cutbefore yy shifted point 0 of xx
cutafter yy shifted point 1 of xx;
endfor
draw ss withcolor 1/2[blue, white];
draw tt withcolor 1/2[red, white];
draw uu withcolor 1/4 green;
label.top("$f(x)=sin(x)$", point 290 of ss) withcolor 1/2[blue, white];
label.bot("$g(x)=\frac12 sin(3x)$", point 295 of tt) withcolor 1/2[red, white];
label.urt("$f(x) + g(x)$", point 350 of uu) withcolor 1/4 green;
drawarrow xx; label.rt("$x$", point 1 of xx);
drawarrow yy; label.top("$y$", point 1 of yy);
for i=-6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7:
draw (down--up) scaled 2 shifted (pi * i/6 * u, 0);
label.bot(pi_sixths(i), (pi * i/6 * u, -2));
endfor
endfig;
\end{mplibcode}
\end{document}
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