Sine and Cosine of i (imaginary unit)

The following is my working for the Sine and Cosine of the imaginary unit, .

Substituting gives

Squaring both sides

Substituing for gives

Rearranging the original equation in terms of gives

Substituing this back into gives

Rearranging for sin(i) gives

Then to find Cos(i): Substituting back into the original equation gives

The problem is that all the sources I can find for the sine and cosine of on the internet say

or and

or .

EDIT: I found my mistake in Cos(i), and now have the same as the internet for cos(i). BUT, I obtained my cos(i) from putting my sin(i) into the original equation and still got the right answer, which makes it even more puzzling.

As you can see, my answers are very close to the others, I just can't figure out where the difference in signs comes from... also, is there any difference if the is put outside the fraction like they have, or on the bottom like I work it to be?

If I've made any typos or not made anything clear enough, just point it out and I'll change the original post.

Thanks, Spud.