Why was ivan iv known as ivan the terrible?

He had a temper that grew worse as he grew older. 
He was cruel to the Russian nobility. 
He was cruel to the boyars. 
He became like that when his wife died of a fever 

When Ivan became a complete autocrat he tortured and executed nobles and clergy alike without trial if he thought they were against him. He created an elite military force who wore all black, rode black horses and used the symbols of a broom and a dog's head to show that they were there to sweep out all the dogs, meaning everyone who they considered disloyal to Ivan. 

This militia, called the oprichniki, tortured and executed thousands in Ivan's name and at his direction. The worst of this group's actions was the massacre of tens of thousands of Russians in Novgorod in 1569 because Ivan thought they were plotting with Poland against him. 

Ivan later began executing members of that militia as well. 

In one incident while in a rage killed his own son.  Source: http://www.answers.com/Q/Why_was_Ivan_IV_called_the_Terrible

The correct answer is b