\documentclass[border=5mm]{standalone}

\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 TEX("$\scriptstyle" & s & f & "\pi$")
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(TEX("$t$"), point 1 of xx);
drawarrow yy; label.top(TEX("$u(t)$"), 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}