The trombone can be assigned to one of the equipment slots. Blowing on the trombone makes a loud sound, which might be useful for attracting robots. The pitch of the trombone can be adjusted with the mouse scroll-wheel. The Artist Class starts with one of these.
Blowing the horn close to robots will confuse them for a short while. In a confused state the robot will not use weapons and is an easy victim to finish off with any of your weapons.