It's not a sin to be angry

In the Christian world, there's a bit of a taboo on anger. Clearly it's not good to be angry, but it's not a sin to be angry.  We get angry because we feel passionately when we have been wronged. It's not bad or sinful to have feelings, whether they're good happy or sad ones. God gave us feelings after all. It's quite possible to be angry and be pleasing to God: I think there's a place for righteous anger. So for example, when we see a prevalence of sin, or a grave injustice, it's perfectly acceptable to feel anger in these situations. If people never felt any such feelings, we'd never be motivated enough to stand up for justice and equality, and for God's Word.

The first instance of anger in the Bible is when Cain offered his offering to God, along with his brother Abel, and God deemed Abel's offering more acceptable.  Cain's feelings were hurt, and he wanted to please God, but because God didn't deem his offering acceptable, he was "angry and indignant, and he looked sad and depressed." (Gen 4v5). Right there and then, God didn't swoop down and smite Cain, saying, "Oh your sinful creature, you are full of anger. You are banished from my sight!"  No, He said: "Why are you angry? And why do you look sad and depressed and dejected? If you do well, will you not be accepted? And if you do not do well, sin crouches at your door; its desire is for you, but you must master it."

God sees Cain is angry but doesn't condemn him for his anger, but instead and asks him why he's angry. 

Right there is where we see the pivotal point of where anger becomes sin. If you do well, you will be accepted, if you don't do well then sin lies in wait. So what should Cain have done to use his anger and do well at that point?  He should have listened to God's question first of all. It's the most important question He could ask Cain. WHY are you angry? The answer Cain should have given was that he was angry because he wanted to please God, but he failed. His offering wasn't worthy and he didn't please God like Abel did, and that was why he was angry. He wasn't angry with Abel, he was angry with himself. The correct introspection should have lead to him doing well and being accepted by using his passion and anger by doing something to remedy the situation - i.e. offer a more acceptable sacrifice to God. 

However, we all know Cain chose to ignore God's question. He let his anger consume him, instead of letting it fuel him towards what God was urging him to do. Instead he went out and killed his brother, letting his anger turn to sin.  

  

Another time God didn't correct someone for being angry is when Moses got angry at the people of Israel (although he did this many times). But specifically I'm thinking about the time he'd been up the mountain with God whilst the people who'd recently been freed from centuries of slavery, unable to worship their God, forced to worship idols, were waiting for the word from their God. He was on his way down with the 10 commandments and what did they do, but create a golden calf to worship! Moses was so angry, he broke the tablets of stone! Ex 32 v 19 "And Moses’ anger blazed hot and he cast the tablets out of his hands and broke them at the foot of the mountain"

Moses was rightly angry. He didn't sin though, he told the people he was going to pray for them and he sought God.  

There was a time though when his anger did get the better of him, and it had grave consequences. Moses had been leading these people, God's people, having lead them out of generations of captivity, however instead of being ecstatic at being free, they complained about everything. They saw major miracles, they had God with them night and day, yet they still complained about God and Moses for bringing them out into the wilderness. It’s clearly not a surprise that Moses was a little naffed off with them. They were complaining about being thirsty, and God yet again came through for them telling Moses, 
"Take the rod, and assemble the congregation, you and Aaron your brother, and tell the rock before their eyes to give forth its water, and you shall bring forth to them water out of the rock; so you shall give the congregation and their livestock drink” (Numbers 20 v 8). 
Now Moses "lifted up his hand and with his rod he smote the rock twice. And the water came out abundantly, and the congregation drank, and their livestock." Blink and you may miss it, but God sees Moses' anger and his sin. Moses struck the rock twice instead of once. He let his anger manifest by misrepresenting God to His people. God loved these people, even though they were grumbling and moaning. Whatever they asked, He provided them. But Moses was getting angry with them, and he manifested his anger by striking the rock twice and he disobeyed God by doing so, and he misrepresented God, alluding to the Israelites that God may be angry with them too. This manifestation of Moses' anger lead to God telling Moses, you "shall not bring this congregation into the land which I have given them."  That's a smack in the chops for Moses - he'd done all God had told him; he'd stood up to Pharaoh; he'd been God's voice to the people; he'd been up the mountain with God and had untold revelations of God's majesty; he'd even asked to see God, and God allowed him to see a tiny glimpse of His back (any more would probably have killed Moses). Yet the result of Moses' anger, even though he was angry for a "good" reason, and God said no, you can't go into the promised land.

Let's jump over to the New Testament, to Ephesians 4 v 26 "When angry, do not sin; do not ever let your wrath (your exasperation, your fury or indignation) last until the sun goes down."

Notice that Paul doesn't say, don't get angry. He doesn't say, when angry you're being sinful. Rather, he sees that as humans, we will get angry, sometimes perhaps rightly or wrongly, but whatever the cause, we are to check ourselves. Jesus got angry at the sinners who were using the temple as their marketplace, dealing and selling and gambling in His Father's house.  It was borne out of passion and we know Jesus never sinned. He immediately did something about it. We must choose not to sin, and he lets us into a little nugget of revelation, that we must not let our anger fester.  This is what Cain did. He focussed on his anger, he let it niggle away at him instead of addressing it and using it to do well. 

We're not supposed to live in a state of anger, don't misinterpret me. Anger produces hormones and responses in us which will lead to stress and health issues if left for long periods of time. It will lead to unforgiveness and you only need to look at Cain to see what a festering anger can lead to....If we ask ourselves the question God asked Cain, "why are you angry", before we even have chance to sin, we can use the passion we feel and do well. Don't feel condemned if you feel angry. God will guide you in how to do well.