A series expansion of (sin(t))/t is???? please help needed along with explantion if possible bt answer is ok?

Question

PLEASE HELP

Answer 1

Well the MacLaurin series for sin(t) is just

t - (t^3 / 3!) + (t^5 / 5!) - (t^7 / 7!) + ...

So dividing each of these terms by t gives

1 - (t^2 / 3!) + (t^4 / 5!) - (t^6 / 7!) + ...

Note that this doesn't work for t=0, though.  sin(0)/0 = indetermined, not 1.