To cogitate means to think deeply and carefully about something. When you cogitate, you're actively working through a problem, turning ideas over in your head, examining them from different angles. You're concentrating and analyzing, not letting thoughts drift randomly through your mind.

A detective might cogitate over the clues in a mystery, sitting quietly while piecing together what happened. A chess player cogitates before making an important move, thinking several steps ahead. When your teacher asks a tough question and you need a moment to really think about it, you're cogitating.

The word has a slightly formal, old-fashioned feel to it. You might hear someone say they need to “go cogitate on that” when they want time to think something through carefully. It's the kind of thinking that takes effort and concentration, like when you're trying to solve a particularly tricky math problem or figure out the best way to help a friend with a problem.

Cogitation (the noun form) is this kind of deep thinking. After much cogitation, you might finally understand why something works the way it does, or come up with a solution that wasn't obvious at first.