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Definition of cocksure : 1. Perfectly safe.
2. Quite certain.

Synonyms:

convinced, overconfident, irrefutable, positivistic, plus, positively charged, positive, prescribed, positivist, confident, confirming, electropositive, incontrovertible

Usage examples:

• As for Inglesby, he might push Eustis under, but he wouldn't have been so cocksure of her if it wasn't for those letters. - "Slippy McGee, Sometimes Known as the Butterfly Man", Marie Conway Oemler.
• You'd like to behave yourself and be good, of course; but you want to be cocksure beforehand that it isn't going to cost too much. - "The Honorable Senator Sage-Brush", Francis Lynde.
• Too jolly cocksure for me. - "The Privet Hedge", J. E. Buckrose.