What does tan(x) and ArcTan(x) mean?

They''re trigometric functions. You can take trigonometry to find out what they mean

Basically, if you have yourself a right triangle, and one of the angles of that triangle is x, tan(x) describes the ratio between the side opposite the angle and the side adjacent to the angle. Arctan(x) is the inverse of that operation, meaning that if you provide it with aforementioned ratio, it gives you the reference angle that produced that ratio.

If I had a picture of a triangle, this would be easier to explain But you really should be Google''ing this, shouldn''t you?

The tangent of an angle x, tan(x), is defined as sin(x)/cos(x). arctan(x) is the inverse of tan(x), that is, tan(x) = y <=> x = arctan(y).

tan means Tangent, it''s a trigonometric function. Arctan is it''s opposite. This link should help:

http://abe.www.ecn.purdue.edu/~agen215/trig.html

Pay attention to Miserables explanation. They aren''t "opposite" functions, but rather inverses such that Tan(ArcTan(x)) = x and ArcTan(Tan(y)) = y. Focus more on the circular properties of these functions, because I find them to pop up more often in gamedev than the geometrical interpretations.