How Do You Derive the FRW Metric for a Closed Universe?

Skye
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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\chi2 + Sk\chi2d\Omega]

using r = Sk\chi = (1/\sqrt{}Ksin(\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 :)
 
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Never mind. I get it. Guess I'm not as rusty as I thought.
 

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