Why is the Csc of (1,0) undefined

I'm not sure what you mean by the "Csc of (1,0)" ...

However, the Csc(0) is undefined because:

          Csc(x)  =  1/Sin(x)

--->   Csc(0)  =  1/Sin(0)

Since the Sin(0) = 0, 1/Sin(0) = 1/0 and 1/0 is undefined; therefore, Csc(0) is undefined.