Does this sentence make sense for the word coquette?:
My friend likes to coquette with most of the guys at school.
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The word "coquette" is a noun, not a verb.
http://dictionary.reference.com/browse/coquette
i thought it could be used for both
...that's what it says on the website
what about..My friend acted like a coquette at the party last night
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Your second sentence is fine.
Go back and look at that dictionary link. Notice the spelling if you plan to use it as a verb, but be aware that's a very rare use.