What is the domain of tangent?

Question

I know that the domain of tangent is all reals except n(pi)/2 where n is any integer...can someone please explain to my why though? and my teacher wrote something like nEodd integers, but the E was curved...and I dont understand. Please help, I have a quiz tomorrow in AP cal and I really need to understand this!

Answer 1

the "curved E " means 'is an element of ' or ' belongs to '...the domain is U( -π/2 + nπ, π/2 + nπ) for n being an integer or all reals except (2n+1)π/2 for n being an integer