Date: Feb 21, 2011 12:26 AM
Author: Colin Campbell
Subject: arc cotangent function--negative values
There seems to be two competing arccot functions "out there".
The more "serious" function has a discontinuity at x=0, where y jumps between pi/2 and -pi/2. Graphs can be seen at:
Perhaps the most authoritative source is the graph at the National Institute of Standards:
where it states: "arccot x is discontinuous at x=0"
The three best trig calculators on the web return values on this curve for negative values of x:
The more "popular" function is a continuous ski-slope through y=pi/2 at x=0. It can be found in books, all the tutoring web sites, and other locations. The most prominent graph can be found at:
It is clear from the graph that this arccot is complementary (sums to a constant value) to the arctan function.
I understand the inverse trig functions are multi-valued and their principal values depend on somewhat arbitrary branch cuts. I suspect the differences come from the way the functions are derived--directly from the cotangent function or indirectly from another inverse function. (I have read one article that states arccot is defined as the complement of arctan.)
Any light anyone can shed on this topic will be appreciated. Thanks.