It is not always the last thing you do which makes them angry, maybe you moved their favorite place to sit in the sun last week and they just noticed because it's been cloudy since then. So you have to look for the cues, one common one is the isolation.
The nonhuman will almost always avoid the person they are angry with until they forget why they are angry. You must give them time to stop being angry before trying to apologize or they may take longer to forget they are angry. However, sometimes they get comfortable where they are don't let you know.
So, you check up on them once in a while, give them some small pets to let them know you are not angry with them, then let them have more time to themselves. Eventually that anger fades and they decide they want more attention, this is when they have accepted your apology and forget to be angry.
The other behaviors can be dangerous or destructive, and these you have to deal with delicately lest they learn them. Knocking pots off the shelves is one of the most common for cats, it's also one that will cost you a few plants. You have to ignore it, do not give them any attention when they do it, pretend they are not there.
It is also good to not clean it up until they are done with their tantrum, they most likely want to see you work. If you ignore the behavior well enough, and long enough, they give up and try something else. If you rush to clean it up and acknowledge the animal in any way, even punishment, then they will know they can get attention from it.
Another common one for both dogs and cats is the wild defecation. They seem to be doing it randomly, but it's not. It is premeditated, unless there is a medical condition. This is the most difficult one to deal with.
If it is a medical problem, you may want to make a vet appointment just in case on this one, then clean it up and let the animal know it's alright. They didn't do it on purpose you have to let them know they are not in trouble for it or they may get angry at you and start doing it even when it's not an accident, and then it becomes a learned behavior.
Sitting in your way is not out of anger, but it can be an apology. Sitting on a keyboard, your lap, or even in your path, is actually begging for attention. Both dogs and cats are notorious for this, and if they were angry a prior to this act, it is an apology from them.
Our human children do this as well, so if you have raised human kids, you know the technique already. Same idea here. Attention is everything to our young, and our domestic animals. It is more valuable than all the riches, and more important than even food. Though there are times when the domestic animals will not want attention, like my Pepper who prefers to mope away from me.
Anyone who has rescued abuse and mistreated animals can tell you, the cycle takes more time to break than bad habits. You have to spoil the animal rotten for a very long time to get them out of that cycle. So don't start the cycle. Ignoring them is the only real punishment that they understand, especially when they want affections. To them, any attention is better than no attention.