if you observe a supernova at redshift $z=2$, does the lightcurve get time-dilated due to the Hubble expansion? if yes, by how much? at what redshift would you need to place a supernova if you want to stretch the lightcurve to last a year?
math bonus: just using a compass and a ruler, it is easily possible to construct $\sin(\alpha)$ and $\cos(\alpha)$ of an angle $\alpha$ (how?). can you construct $\sinh(\alpha)$ and $\cosh(\alpha)$ as well for arbitrary angles $\alpha$?