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simple Sin

It is surprising a bit, by numerical computation Sin[ t] has a
different series representation, is not even an odd function of t !
Looks like has a different chemistry.

NDSolve[{y''[t] + y[t] == 0, y'[0] == 1, y[0] == 0 }, y, {t, 0, 2 Pi}]
sin[u_] = y[u] /. First[%]
Plot[sin[t] - Sin[t], {t, 0, 2 Pi}]

Series[{sin[t], Sin[t]}, {t, 0, 8}]

Also, why do we not get an expansion of  sin as Series[Im[Exp[I*t]],
{t, 0, 8}] ?



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