The MacLaurin series for [tex]e^x is 1+ x+x^2/2+ x^3/3!+ ...

What do you get when you subtract 1 from that.

The MacLaurin series for sin(x) is x- x^3/3!+ x^5/5!+ .... If you divide the previous series by that, do you see that you can cancel an "x"? Then, as x goes to 0, all but the constant terms will disappear.