The tendons of the rotator cuff, not the muscles, are most commonly involved, and of the four, the supraspinatus is most frequently affected, as it passes below the acromion. The role of the supraspinatus is to resist downward motion. The supraspinatus resists downward motion while the shoulder is relaxed as well as when carrying weight. Such a tear usually occurs at its point of insertion onto the humeral head at the greater tubercle. Even though the supraspinatus is the most commonly injured muscle of the four muscles in the rotator cuff, the other three muscles that comprise the rotator cuff, the infraspinatus, teres minor, and subscapularis, may also be injured.

Is it true that is the supraspinatus tendon part of the rotator cuff?
yes