what does tan mean

Your are correct HSC.....I hadn't thought of that !     

Tangent is a trigonomic function. It is also the SLOPE of an angle.

It can be defined as Opposite leg / Adjacent leg in right triangles. 

It is also defined as  SIN / COS  for a given angle .

Also in a function a "tangent" of a certian point on the function is an imaginary linear function that does not touch any other point... ever.

You also thought of some very good points. Props to you :)