I'm really interested to know as I'm trying to work out how Euler Angles work and I believe it would help to know what ArcTangents are & how they work. I've visited many different pages for help but cannot get my head around it. I'd like it if examples were also given.

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Have a look at this question on StackExchange Game Development: https://gamedev.stackexchange.com/questions/14602/what-are-atan-and-atan2-used-for-in-games

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Knowing that ArcTangent is simply the Inverse of Tangent (Tan^-1) is very helpful & that link was very clear.