Other forms: sanguinely; sanguines
If you're sanguine about a situation, that means you're optimistic that everything's going to work out fine.
Sanguine is from Latin sanguis, "blood," and it originally meant "bloody" — in medieval medicine, it described someone whose ruddy complexion was a sign of an optimistic outlook. That was back when people thought that "bodily humors" like blood were responsible for people's attitudes. Now that we no longer believe in humors, sanguine has settled down as a fancy way to say someone is cheerfully confident that things will work out well.