To change one's mind, especially to begin to agree or appreciate what one was reluctant to accept at first.(verb)
To regain consciousness after a faint etc.(verb)
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Use "come around" in a sentence
"Delaware would come around as well with the arrival of a third delegate, Caesar Rodney, who was then hurrying to Philadelphia."
"When I come around the next time, Sue Doss is at my bedside."
"And, for the record, I did get Harry to come around to the idea before I went through with it, and I know he would agree that my boob job was a good decisionit made me feel like a woman again and resuscitated our sex life!"