Re: Very strange behaviour of ArcTan[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg102674] Re: Very strange behaviour of ArcTan[]*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Tue, 18 Aug 2009 06:09:10 -0400 (EDT)

On 8/17/09 at 8:06 AM, lehin.p at gmail.com (Alexey) wrote: >Hello, I just have discovered some strange (buggy?) feature of >ArcTan[] function in Mathematica 5.2. Try the following; >In[72]:= ArcTan[.5,$MachinePrecision] ArcTan[.5] >Out[72]= 1.53947 >Out[73]= 0.463648 >The expression ArcTan[.5,$MachinePrecision] must (?) give an error >but in really gives some strange output without any error >messages... What do you think about this? It appears the result you are getting is entirely consistent with the documented behavior of ArcTan which I am guessing you have not looked at. Specifically, the documentation states ArcTan[x,y] computes ArcTan[y/x] paying attention to the quadrant (x,y) is in. Since $MachinePrecision returns a numeric value there is no error generated when evaluating ArcTan[.5, $MachinePrecision]. And since $MachinePrecision is a positive value In[6]:= ArcTan[.5, $MachinePrecision] == ArcTan[$MachinePrecision/.5] Out[6]= True