A friend of mine told me that cats show their emotions through their tail.
I have cats that are angry 'shake' their tails, but is it true for all their emotions?
Cats do show their emotions through their tails. However, the tail isnt enough to read their emotions perfectly. You really have to observe an individual cat over time to link their emotions to their behaviors.
For one of my cats, an angry tail shake could mean she is annoyed or content. It can also mean she is really interested in something. While my other cat doesnt shake his tail in the same way at all.
The tail is one indicator, as part of the cat's overall posture and motion.
And of course there's the question of whether we're seeing all the important details. For example, there are at least two distinct cases of bushy tail. There's the fear/anger tail, with the classic "bottle brush" shape, which starts fluffing from the tip of the tail inward. But There's also a version which starts fluffing from the base of the tail and progresses outward. I've heard some cat owners refer to this as "happy tail", but in my experience it seems to be associated with dominance-play. One of my cats does this when we're "wrestling"; he also sometimes does it when he's about to paw my face.
I agree with Keltari. There are basic gestures and each individual might do some of them slightly differently.
Tail up: I'm happy
Tail flicking: I'm annoyed
Tail twitching: excited, agitated, about to spray...
Tail bushy: alarmed, afraid, battle ready
Tail down: depressed, submissive
But an old or arthritic cat can hold its tail down because it is difficult to lift... So these are rough guidelines, again each cat does some of these things somewhat differently.