Re: Another damn simplifying problem: ArcTan
- To: mathgroup at smc.vnet.net
- Subject: [mg59974] Re: Another damn simplifying problem: ArcTan
- From: Mathieu McPhie <m.mcphie at fz-juelich.de>
- Date: Sat, 27 Aug 2005 04:11:04 -0400 (EDT)
- References: <dek7hq$a2t$1@smc.vnet.net> <demm3s$rd1$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi all again, By drawing a little diagram I have cunningly devised the following arctan indentities, which I think M. should know, you know? 1. ArcTan[x,y] + ArcTan[x,-y] = 0, for all real x and y 2. ArcTan[x,y] + ArcTan[-x,y] = pi, for all real x and y > 0 3. ArcTan[x,y] + ArcTan[-x,y] = -pi, for all real x and y < 0 I can get M to Simplify the 1st expression, but only for x > 0, not the general result, i.e. Simplify[ArcTan[x,y]+ArcTan[x,-y],x>0] = 0 I can get Ma to reproduce the first general by the following complicated expression Simplify[Factor[TrigToExp[ArcTan[x, y] + ArcTan[x,-y]]] /. Log[x_] + Log[y_] -> Log[x y]] = 0 But using the same proceedure with the 2nd/3rd expression yields the answer pi, regardless of the sign of y. Simplify[Factor[TrigToExp[ArcTan[x, y] + ArcTan[-x,y]]] /. Log[x_] + Log[y_] -> Log[x y]] = pi WTH? Anyone got ideas here? Cheers, Mat Mathieu McPhie wrote: > Sorry, I got my x's and y's mixed up, and so I was more curious about > why "M" can't simplify the following: > > Simplify[ArcTan[x,-y]+ArcTan[x,y]] > > This can be simplified by choosing x > 0, and not if x < 0. Which > according to the range of the ArcTan function should also evaluate to 0. > > Cheers, Mat