I guess this is what my teacher was talking about...
Back to my question though; if the domain of was restricted to would my original answer be correct?
By the way, I had a look at your paintings Grandad. They are amazing :)
You are quite correct - there does seem to be a convention that distinguishes between tan and Tan (and, indeed, sin and Sin, etc).
The use of the upper-case initial letter, then, restricts the domain of the functions to their principal values. This has the effect of making the functions one-to-one, and therefore makes it possible to define the inverse functions. In that case, the domain of
would indeed be
Since this upper- and lower-case convention appears not to be very widespread, I should use it with caution if I were you.