The triceps muscles are responsible for performing the action on one side of the joint and hence they are termed as agonist while on the other hand the muscle which opposes this action is called an antagonist.
During elbow flexion, triceps causes the action by contracting and hence it acts as agonist. This muscle lies on the posterior side of Humerus and work as a third class lever.
The triceps brachii is considered antagonist and agonist according to the action it perform at particular muscle action. The antagonist action is due to the presence on the opposite end of the the elbow joint and can restrict the elbow flexion.
If the case is about the active elbow extension as asked in the provided question it is agonist due to the support of action of the extension.
