Math Help - complex analysis integration

can anyone explain to me the parameterization of the semi circle on this page

Contour Integral

like why is it -cos(t) + isin(t) as opposed to just cos(t) + isin(t).

Thank you.

Because you are going the other way (look at the arrows).

but why is the cosine negative and not the sine?

shouldn't the direction affect both sine and cosine?

Oh, that is because you are taking the conjugate.

i mean, right before you find the conjugate. initially, it is

-cos (t) + isin (t). Thats the part I dont understand. Why is the cosine negative and the sine positive.

I understand the conjugate of that becomes

- cos (t) - isin (t).