Broken? Tryndamere has:
A crit passive witch is inferior to yasuos after they have gotten shiv and vastly inferior after IE. Note that yasuo has one more passive to boot.
A soft cc slow/ad-kill that is unreliable as it is situational at best to get the most of, it also does practically nothing to mitigate damage from any non ad champ.
The spin of doom, since if he uses it to engage he can kiss his *ss goodbye if he doesn't get the job done.
An ult that makes him unkillable, note, not invulnerable like kaylies, the cooldown at first level is also immense, one of the longest in the game.
When you see it on paper, he doesn't actually seem so bad. But put into practice, while Tryndamere is a very strong skirmisher, he is without doubt the absolute worst teamfighter in the game, therefore his role is generally to push which he does well, but why would you ever pick him over someone who has pushing capabilities and can rejoin their team in a fight in an instant, like shen? Or someone who both push and tank for their team, or disrupt the enemy team? Because of this, if Tryndamere fails his lane he is totally doomed, and will be useless the entire game, he is feast or famine, more so than ex. Riven, who even if behind, can make catch plays for their team by flanking the backlines and getting an aoe stun of on key targets to turn the teamfight, all options like that are out of Tryndameres reach as 90% of his capability of affecting the opposing team comes from autos.
As for the jungle, why would you ever pick him over Yi, who has similar gameplay style, when Yi has, 3x faster clear (I kid you not), better chase and the ability to evade any and every cc in the game with a well timed Q and thus far better ability to take out key targets?
Ergo, yes, he is broken, plainly brokenly BAD! and in a horrible spot right now, he needs something to get him going,
I'd like to see his mocking shout do half the slowing effect against targets that are facing him, perhaps that would allow him to shine a little more.
Because right now, he's just so horrible.