# FRW metric for closed universe

Hi, I'm new to Physics Forum and wasn't really sure where to post this since its not strictly speaking a homwork question. So if it happens to be in the wrong place I apologise.

I was looking through some lecture notes from when I did my Physics degree years ago and come across a problem involving the FRW metric.

Basically i'm trying to get from

ds2 = dt2 - a(t)2[(dr2/(1-Kr2))+r2d$$\Omega$$]

to

ds2 = dt2 - a(t)2[d$$\chi$$2 + Sk$$\chi$$2d$$\Omega$$]

using r = Sk$$\chi$$ = (1/$$\sqrt{}K$$sin($$\sqrt{}K$$$$\chi$$)

After I competed my degree I took a bit of a break from Physics so I'm quite rusty at this stuff. Would appreciate any help i can get :)