Why is the domain of arctan power series |x|<=1?

1. Aug 12, 2008

linyen416

Why is the domain of arctan power series |x|<=1?
i understand why a power series has the domain |x|<1, but why is the power series of arctan |x|<=1?
thanks!

also, why are domains of the taylor expansions of coshx and sinhx: for all x?

2. Aug 12, 2008

arildno

What do you know about the complex number plane?

3. Aug 13, 2008

mathwonk

are you kidding? arctan is the integral of 1/(1+x^2). what makes it look undefined at some points of |z| = 1?