Super telephotos are not always the answer to getting those frame-filling images so desired by art directors for use on magazine covers. You still need to get close to your subject.
The secret of approaching any wild animal is for it to accept you as part of its natural surroundings and not feel threatened by your presence.
When approaching members of the deer and sheep family, I often use what I call the "grazing approach." It's a technique I learned while observing herds of elk. Individual animals were constantly moving about, yet the herd appeared to stay in one place. Despite appearances, however, the entire herd was gradually advancing toward ungrazed areas.
Once you have spotted a particular subject, remain where it can see you. Do not attempt to get any closer at first. Sit down or mill about, but stay where you are at least five minutes; then you can begin your approach.
Never walk directly to your subject. Pick a direction of travel that will take you past the animal. After going some distance, turn around and walk past the subject again, altering the direction of travel so you pas a few feet closer. Continue this zigzag approach until you are within photographic range.
While zigzagging, act as if you were grazing. Walk slowly, stop often and mill about, occasionally even sitting down for a minute or two. Watch for any change in your subject's behavior while at the same time avoiding direct eye contact. Stop the moment you detect any change. You will avoid stressing your subject as long as it can anticipate your actions and not feel threatened.
Regarding stress, it is best to approach most members of the deer and sheep family from the downhill side. Since these species tend to escape predators by fleeing uphill, this avoids cutting off any potential escape route that in turn may cause them to exhibit signs of stress. I have found mountain goats are often the exception to this rule, appearing to be more comfortable when approached from above.