Hello Stroodle Originally Posted by

**Stroodle** 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

$\displaystyle \text{Tan }(2\arcsin(x))$

would indeed be $\displaystyle \left ( -\frac{\pi}{2},\frac{\pi}{2}\right )$

Since this upper- and lower-case convention appears not to be very widespread, I should use it with caution if I were you.

(Thanks for the comment about the paintings. If you just looked at the ones on my profile, you'll find some more in the Chat Room at http://www.mathhelpforum.com/math-he...-painting.html.)

Grandad