Given these two expressions
1) $\sinh{d}=\frac{\sqrt{t^2−x^2}}{\sqrt{1−(t^2−x^2)}}$
2) $\sin{d}=\frac{\sqrt{t^2−x^2}}{\sqrt{1+(t^2−x^2)}}$
for distance $d$ from the origin $(0,0)$ to point $(x,t)$, which of these two options applies to de-Sitter space and which to anti de-Sitter space? For definiteness, assume $t$ is time and $(x,t)$ is time-like, that is $t^2-x^2$ is positive.
Does option (1) correspond to a space with the positive curvature and (2) to the negative one?