Tan (pi/2)

We most of the time think tan(pi/2) = infinite , 

and our reasoning is 

tan (pi/2) = sin(pi/2) / cos(pi/2) = 1/0 = infinite , this expression is true 

but when we find value of tan(pi/2) its exactly not defined, since it has two values (+/- infinite)[check image] which cannot be of any function [Functions have only one image].

And having two values at (pi/2) we treat this as not-defined.

SO WHEN EVER SOMEONE ASK TO YOU (generally in interviews) :

What is TAN , a function or relation: Answer is Relation

And at odd multiple of (pi/2) "tan" is not defined.