Arousing emotions in writing is really hard. But there is always a pattern out there you can try and follow.
For the emotion of anger you can take an example at internet trolls and their drive to instill flamewars on forums.
Their motivation is mostly selfish and seek pleasure in sowing discord.
Often they feel miserable and/or jaelous and need an outlet as a release for their own feelings.
They then seek a forum, a thread, a post they can victimize and can respond to maximum effect. Instead of clearly answering a question or responding to the post they will insult and post a conflicting opinion of the poster. In seeking conflict openly there will be responses by either the OP (Original poster) or people that feel they need to defend the OP. This instilled response is not always without an opinion of their own. This could then cause the troll or other people to respond. A chain reaction is what follows and can end up in a flame war.
So what is the most effective way of causing anger in writing?
Make sure the reader has some sort of opinion or feeling and then try to bash it, insult it, and contradict it. It being that opinion or feeling, the more ridiculous or loaded the better.
Have the reader care about something and then kill it off in a single stroke.
Do something the reader is morally against.
I hope it helps.
EDIT: (an example)
Context is everything!
So before I give an example I will give a fictional case with finctional people.
Andrew is an amateur swimmer. He competed in a regional qualifier for the nationals. To enter match he had won a preliminary match.
Unfortunately he was placed second but he was still very happy about his result.
So happy he wanted to share it on his swimming forum which he had used to learn the best techniques and helped him a lot honing his skills.
"Second place at regionals:"
Hello fellow forum people
I would like to thank you for all your teachings and support for the regionals I entered.
I even managed second place!
Couldn't have done it without you guys, maybe next time I can hit the nationals.
It is important that the OP shows some kind of emotion about the subject. Happiness works nicely. But it also works with displeasure, and in some cases it works even better.
Next up, the troll.
Bob, also an amateur swimmer, a very fanatical one. Every day and every hour he could spend, he spent training for the upcoming swimming matches. Obviously he would make nationals like last year. No competition is a match for him.
He lost to Andrew in the preliminary. It was real close but still Bob was extremely angry about it.
He is also a member of the swimming forum.
He saw the post of Andrew about his result.
Second place. I knew he wasn't good enough. If only he just let me win. At least I would be able to reach the finals.
"Re: Second place at regionals:"
I'm sorry to hear you reached second place.
I guess you didn't have the skills to win just yet.
You shouldve given up and let me win in the preliminaries at least I could beat that number 1 of the regionals.
This is Bob's response.
He is angry and wants Andrew to feel bad.
He shows pity for Andrew and wants to make him feel bad by telling him he lacks skill. On the other hand he also wants to tell him that he is angry and tells him he shouldn't have competed in the first place.
The effect of a negative post like this is usually unpredictable on a forum.
You can get justice warriors trying to defend the OP. Telling him he did just fine getting second place. Others will feel pity for the troll. Others will be angry at the troll for reacting so negatively.
But for the sake of the emotion anger I will make an example of a reaction to the troll.
Meet Carl, a swimming enthousiast. He likes the competition but never really got the time to try swimming competatively. He often reads the swimming forum and enjoys reading about people getting results.
He sees the post of Andrew. Someone who was actively asking questions on the forum. Carl even helped Andrew with some of his techniques.
He got second on the regionals! That is a nice result. I bet my techniques helped him well. Let's read his post.
Carl reads the post and is happy at first. Until he reads the response of Bob, our troll.
How could he say that! He won fair and square and probably did the best he could.
"Re: Re: Second place at regionals:"
Well Bob, he beat you fair and square.
I guess you just wasn't good enough for Andrew.
Just let him enjoy his accomplishment!
A valid response for someone angry on a forum right?
All loaded with emotion.
Again context is everything!
Without the preknowledge of what happened it is hard to tell which emotion is instilled and what is written. This reply of Carl can also give the troll an opening to respond until a chain reaction of negativity degrades Andrews positively toned post.
I hope this example will give you an idea of what I meant. There are a million (other) ways to describe this. But writing about emotions and instilling emotions is really hard!