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\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
vardef pi_quarters(expr n) =
save s, f, q; string s, f; numeric q;
s = if n < 0: "-" else: "" fi; q = abs(n);
if q mod 4 = 0:
f = if q > 4: decimal 1/4 q else: "" fi;
elseif q mod 2 = 0:
f = "\frac{" & decimal 1/2 q & "}{2}";
else:
f = "\frac{" & decimal q & "}{4}";
fi
"$\scriptstyle" & s & f & "\pi$"
enddef;
beginfig(1);
numeric u, pi; u = 50; pi = 3.141592653589793;
path xx, yy;
xx = (3.5 left -- 3.6 right) scaled u;
yy = (1.1 down -- 1.2 up) scaled u;
path ss;
ss = origin for t=1 upto 360: -- (t, sind(t)) endfor;
ss := ss shifted 360 left & ss;
ss := ss xscaled (pi/180) scaled u;
drawoptions(dashed withdots scaled 1/4);
draw ((1/4 pi, 0) .. (1/4 pi, sind(45))) scaled u;
draw ((1/2 pi, 0) .. (1/2 pi, sind(90))) scaled u;
draw ((3/4 pi, 0) .. (3/4 pi, sind(135))) scaled u;
drawoptions();
draw ss cutbefore yy shifted point 0 of xx
cutafter yy shifted point 1 of xx
withcolor 3/4 blue;
draw ss shifted (-1/2 pi * u ,0)
cutbefore yy shifted point 0 of xx
cutafter yy shifted point 1 of xx
withcolor 2/3 red;
drawarrow xx; label.rt("$t$", point 1 of xx);
drawarrow yy; label.top("$u(t)$", point 1 of yy);
for i=-4, -3, -2, -1, 1, 2, 3, 4:
draw (down--up) scaled 2 shifted (pi * i/4 * u, 0);
label.bot(pi_quarters(i), (pi * i/4 * u, -2));
endfor
endfig;
\end{mplibcode}
\end{document}
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