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1. To become calmer. Don't talk to your mother like that! Go to your room and cool out! I'm sorry for my outburst—I just need some time to cool out.
2. To cause someone to become calmer. In this usage, a noun or pronoun can be used between "cool" and "out." If you insist on talking to your mother that way, I think a punishment is the only thing that will cool you out. That break seemed to cool him out—he's no longer yelling at the staff.
cool someone out
Sl. to calm someone; to appease someone. Cool yourselves out, you people. We gotta be sensible. The manager appeared and tried to cool out everybody, but that was a waste of time.
in. to calm down; to relax. (see also cooled out.) Now, just cool out, man. This will pass.