Step 1: Identify the three pockets above the aortic valve. Two of them are coronary sinuses and one is the non-coronary (posterior) sinus that supplies no coronary vessel.
Step 2: The right coronary sinus, positioned anteriorly, is the origin of the right coronary artery. For this reason the right aortic sinus and the anterior aortic sinus are the same structure.
Step 3: The left coronary artery springs from the left posterior sinus, while the so-called posterior or anterior coronary sinus options do not correctly describe a coronary artery origin. The coronary sinus on the heart surface is a venous channel, not an aortic sinus.
Step 4: The right coronary artery therefore originates from the right aortic sinus.\[\boxed{Right\ aortic\ sinus}\]