That is the image that Ronald "we will not deal with terrorists" Reagan projected.
The truth is that President Reagan and his staff cut a deal with the Iranian terrorists. In order to negotiate the release of American hostages held by Lebanese terrorists who were backed by Iran, Reagan was willing to sell the Iranian terrorists arms so they could spread terrorism and threaten more people. These arms weren't shipped directly from the USA to Iranian terrorists. That would have been illegal. Reagan's team worked out a deal where the arms were sold through third parties to the Iranians.
Not satisfied with just supporting and spreading Iranian terrorism, Reagan's team wanted to also support a bunch of narco-terrorists, called the Contras. Monetary and material support for the Contras was prohibited by law. The Republican administration didn't like the left leaning Sandinista government of Nicaragua and wanted to support a right wing revolution so a puppet government could be installed. Similar to the support for the Shah's puppet government in Iran that lead the Iranian people to hate America so much.
American intelligence officials syphoned some of the money made selling arms to Iranian terrorists, to the drug trafficking Contras in Nicaragua who opposed the left leaning government there. The Republicans called these drug trafficking scum 'Freedom Fighters'.
The Iranian revolutionary terrorists were completely aware of the arms deal Reagan had made with them, although the American people were not.
So when the Iranians saw President Reagan give the icy stare and say those scary words, the Iranians were in no way frightened. The Iranians knew Reagan was a liar with no morals. A man who would sell out his own principles in order to gain power and high office. They labelled him "The Great Satan" because of his skill at lying.
The American people were unaware of the deal that Reagan had made to give arms and money to the Iranian terrorists, and were unaware that the freedom fighters were really drug traffickers sending poison to the streets of America and spreading terrorism throughout Central America. The American people saw Reagan as a tough guy who would never deal with terrorists and never waiver on truth, justice and the American way.
So once you read up on the Iran Contra affair, you will realise that the tough talk and that icy stare threatening the Iranian terrorists was one of Ronald Reagan's best acting jobs.