Domain of ArccotDate: 05/23/2002 at 21:47:58 From: Lester Penning Subject: ArcCot Range I have a good understanding of trig, but I just want to know why the range of the arccot is between 0 and Pi and not Pi/2 and -Pi/2 like the range of arctan is..... Date: 05/24/2002 at 08:42:03 From: Doctor Peterson Subject: Re: ArcCot Range Hi, Lester. In order to invert a trig function, we first restrict it to a domain on which it takes all its possible values, once each; then we invert the restricted function, whose range is then that restricted domain. Look at a graph of the cotangent function, and you will see that although between -pi/2 and pi/2 it takes all its possible values, and takes each value only once, there is one problem with this choice: it is not continuous (or even defined) on this entire domain, but is undefined at 0. The domain would then have to be -pi/2 < x < 0 or 0 < x <= pi/2 To avoid this, we instead choose the domain 0 < x < pi which is cleaner to work with, making a continuous function defined over the entire domain. Inverting that, we get the arccot function you know. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 05/24/2002 at 16:22:26 From: Lester Penning Subject: ArcCot Range Question submitted via WWW: Thank you Doctor Peterson for your quick response. The ArcCot range is now clear to me. Thanks again. |
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