Apparently I'm a tenor, but most of my favorite singers are baritone...

I've always loved to sing, and wanted to take lessons. I happen to posses a tenor voice, which explains why imitating Bruce Dickinson when I was younger was so fun for me. I have it easy with the high notes, but my music tastes have kinda changed. I have a friend who is trained in classical music and has amazing hearing, so I asked him what voice type do I have, he asked me to sing my lowest and highest notes, and he concluded I'm a tenor.

I'm a guitarist who is currently very much influenced by Soundgarden, Clutch, A Perfect Circle and Puscifer, and I'm working on a solo project. I find it really hard to sing in tune with Chris Cornell when I play Soundgarden covers.

Is there anyway to deal with this? How can I improve my lower notes?