Final answer:
The Cuban dance that originated in New York City and became popular in 1975, later featuring in Saturday Night Fever, is the Salsa.
Step-by-step explanation:
In 1975, a Cuban dance that originated in New York City and became popular was the Salsa. This dance was featured in the movie Saturday Night Fever, which showcased various dance styles and rhythms that captured the lively atmosphere of the era. The Salsa is a vibrant representation of the cultural melting pot in New York during that time, heavily influenced by Latin American rhythms and especially by the music from Cuba and its Caribbean neighbors.