Hair with tapered end could very well be normal....
My mom has thick hair to about mid-back length (27 inches or so). Many of the hairs she sheds have tapered ends, and all are not 27 inches in length, some are considerably less. The anagen phase is not static, but very much dynamic and adjusts itself relative to the length of the haircut. If you keep cutting all the hairs on your head except one hair (not really easy to do in practice, just a theoretical supposition) to a certain length, do you think the uncut hair will keep growing and growing till its maximum length? Of course not. It will fall out at a length equal or slightly less than that of the surrounding hair. Also, all non-balding people's scalps contain a few short hairs which never grow very long. The ratio of the long terminal hairs to these short hairs (in non-balding people : it is obviously much less in balding people) is around 7:1. So you have to count both the natural vellus hairs and the uncut terminal hairs which shed according to the haircut. I even once read somewhere that it is possible for the same follicle to intermittently produce short or long hair, without any intervention from medication.
Take my case. I am not thinning at all (no scalp visible when wet), yet I shed some short hairs with tapered ends. EVEN MY SIDES AND BACK shed a few such hairs. The catch is that nearly all of these hairs are pretty much as thick as my normal terminal hairs.
In short, you cannot tell whether an individual hair is miniaturizing, or has miniaturized, by just examining it. It's a matter of degree - there is no sharp dividing line between "miniaturizing" hairs and terminal hairs. Even the baldest men have a few good strong terminal hairs on the top of their heads, don't they? Similarly even the men with thick heads of hair have a few thinner or shorter hairs. You cannot look at one hair , or two hairs, or ten hairs , or even fifty hairs taken randomly from all over the scalp of a person and say " The person who shed these hair(s) is (or is'nt) balding." How do you tell whether a man is balding or not? Obviously, by examining all the hair in the suspected area with a general glance. However, if you shed a lot of shorter AND thinner hairs with tapered ends, and you can see through to the scalp WHERE YOU COULD'NT BEFORE UNDER THE SAME CONDITIONS OF LIGHTING, WETNESS, OILINESS ETC. then you are thinning.
To conclude, DON'T LOOK AT THE QUALITY OF HAIR YOU SHED. To define thinning or balding, you look at what remains on the scalp, not what has shed from it. If your hair is visibly thinning in the Norwood pattern, only then is it a cause for worry. Otherwise, just relax.
Cheers,
Arjun