On Mon, Sep 19, 2005 at 02:04:00PM +0200, Michael Kerrisk wrote: > Andries, > > Could you comment on the following please -- I don't remember > enough of my maths... > > Cheers, > > Michael
Ramiro is right - that is, his text is much better than the present text. However normalizations differ. It is true that tan(carg(z)) = cimag(z) / creal(z), almost by definition. Taking atan() on both sides yields atan(tan(carg(z))) = atan(cimag(z) / creal(z)) but it is not precisely true that atan(tan(x)) = x. The tan() function is periodic with period pi, and atan() returns an answer in (-pi/2,pi/2], so atan(tan(x)) returns the value that is congruent x mod pi and lies in this interval. In particular, atan(tan(carg(z))) returns a value that is congruent carg(z) mod pi and lies in (-pi/2,pi/2]. On the other hand, carg returns a value in [-pi,pi] and if that return value does not lie in (-pi/2,pi/2] then carg(z) and atan(cimag(z) / creal(z)) will differ by pi. In other words: you may write "One has tan(carg(z)) = cimag(z) / creal(z)." Andries >> Von: Ramiro Aceves <[EMAIL PROTECTED]> >> An: [EMAIL PROTECTED] >> Betreff: Bug#326720: carg(3) man page error >> Datum: Mon, 05 Sep 2005 12:19:14 +0200 >> >> Package: manpages-dev >> Version: 1.70-1 >> >> There seems to be en error in carg(3) man page, DESCRIPTION chapter. >> >> "One has carg(z) = atan(creal(z) / cimag(z))" >> >> is wrong and should be : >> >> "One has carg(z) = atan(cimag(z) / creal(z))" >> >> Hope this helps. >> >> Thank you very much. >> >> Ramiro. -- To UNSUBSCRIBE, email to [EMAIL PROTECTED] with a subject of "unsubscribe". Trouble? Contact [EMAIL PROTECTED]
