Hold your arm out so that it is completely extended. the triceps brachii is causing the extension, so it is acting as what? antagonist agonist synergist

I believe the triceps brachii is acting as an agonist. The triceps is an extensor muscle of the elbow joint and antagonist of the biceps and brachialis muscles. It can also fixate the elbow joint when the fore arm and hand are used for the fine movements. For example during elbow extension the triceps Brachii acts as the Agonists while the Biceps Brachii acts as the Antagonist.