supernovae at high redshift

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 \(\alpha\)?