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The term was coined in the 1960s and was used fairly informally. Though the combining form uni- is from the Latin unus meaning one, the term seems to have been influenced by words such as united and universal where the uni- prefix takes on the sense of shared. In this sense, it can be seen as meaning shared by both sexes.
Hair stylists and beauty salons that serve both men and women are often referred to as unisex. This is also typical of other services that traditionally separated the sexes, such as clothing shops or a public toilet.