\begin{tikzpicture}

\begin{axis}[
tick align=outside,
tick pos=left,
title={Simple plot},
x grid style={white!69.01960784313725!black},
xlabel={t},
xmajorgrids,
xmin=0, xmax=6.28318530717959,
xtick style={color=black},
y grid style={white!69.01960784313725!black},
ylabel={sin(t)},
ymajorgrids,
ymin=-1.15616216792467, ymax=1.15616216792467,
ytick style={color=black}
]
\path [fill=black, fill opacity=0.2, very thin]
(axis cs:0,-0.1)
--(axis cs:0,0.1)
--(axis cs:0.628318530717959,0.687785252292473)
--(axis cs:1.25663706143592,1.05105651629515)
--(axis cs:1.88495559215388,1.05105651629515)
--(axis cs:2.51327412287183,0.687785252292473)
--(axis cs:3.14159265358979,0.1)
--(axis cs:3.76991118430775,-0.487785252292473)
--(axis cs:4.39822971502571,-0.851056516295154)
--(axis cs:5.02654824574367,-0.851056516295154)
--(axis cs:5.65486677646163,-0.487785252292473)
--(axis cs:6.28318530717959,0.0999999999999998)
--(axis cs:6.28318530717959,-0.1)
--(axis cs:6.28318530717959,-0.1)
--(axis cs:5.65486677646163,-0.687785252292473)
--(axis cs:5.02654824574367,-1.05105651629515)
--(axis cs:4.39822971502571,-1.05105651629515)
--(axis cs:3.76991118430775,-0.687785252292473)
--(axis cs:3.14159265358979,-0.0999999999999999)
--(axis cs:2.51327412287183,0.487785252292473)
--(axis cs:1.88495559215388,0.851056516295154)
--(axis cs:1.25663706143592,0.851056516295154)
--(axis cs:0.628318530717959,0.487785252292473)
--(axis cs:0,-0.1)
--cycle;

\addplot [semithick, black]
table {%
0 0
0.628318530717959 0.587785252292473
1.25663706143592 0.951056516295154
1.88495559215388 0.951056516295154
2.51327412287183 0.587785252292473
3.14159265358979 1.22464679914735e-16
3.76991118430775 -0.587785252292473
4.39822971502571 -0.951056516295154
5.02654824574367 -0.951056516295154
5.65486677646163 -0.587785252292473
6.28318530717959 -2.44929359829471e-16
};
\end{axis}

\end{tikzpicture}
