how did the united states react to the soviet unions aggression in cuba
how did the united statesreact to the soviet unions agression in cuba
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I think William slightly misunderstood your question because of the way it was worded, but his answer is accurate. It sounds like asking specifically about the Cuban Missile Crisis (which you're free to google for a more detailed answer), which was the first instance in the Cold War where actual use of nuclear weapons was a real possibility. Just prior, the US had placed missiles in range of the USSR as well as attempted to overthrow Castro's government in Cuba. This led the Soviet Union and Cuba making a secret agreement to place Soviet-provided missiles in Cuban water territory; the intermediate-range missiles were definitely in range of striking US soil and JFK's administration had to choose how to respond to the threat.
The short answer is this: JFK decided to negotiate while taking defensive-only military action, based in part on the doctrine of Mutual Assured Destruction (i.e., nuclear war could obliterate all parties involved and therefore made military aggression too risky). For more details on the defensive action/negotiations/outcomes, check an encyclopedia or good internet resource. I don't want to violate academic honesty by naming the strategies.
Actually, I don't believe the Soviet Union acted aggressively in Cuba. Fidel Castro invited them there. There would have been no reason for the Soviet Union to behave aggressively. What alarmed the United States was the USSR's placement of missiles in Cuba. This act was again carried out with the full knowledge and blessing of Fidel Castro.