What should be the correct range of acot function

[Wes Loewer]

There is no consensus on the range of the acot(x) function.

Using -pi/2 < y < pi/2 comes from defining acot(x)=atan(1/x), consistent with asec(x)=acos(1/x) and acsc(x)=asin(1/x)

Using 0 < y < pi comes from defining acot(x)=supplement of atan(x), consistent with acos(x)=supplement of asin(x) and acsc(x)=supplement of asec(x).

Most US textbooks use (0,pi), but a few use (-pi/2,pi/2), and many simply don't mention acot at all. Each has its advantage: (0,pi) is continuous but (-pi/2,pi/2) preserves odd symmetry and can be calculated more precisely for negative values of x.

I bring up this issue in my Precalc class each year and have the students argue for their preference. Makes for a fun discussion.

The nice thing about standards is that you have so many to choose from. ~Andrew Tanenbaum

----
Edit: Sorry, I meant "complement" above, not "supplement." That's where the "co" in cosine, cotangent, and cosecant comes from.