ACOS logarithmic form
05-01-2016, 03:58 AM
Post: #18
 Claudio L. Senior Member Posts: 1,830 Joined: Dec 2013
RE: ACOS logarithmic form
(04-30-2016 08:57 AM)ljubo Wrote:  ...it is interesting question why they have chosen this exact principal branch - or in other words, what would be broken or "ugly" if principal branch would be different, especially if they would took Im(ARCCOS(z))<0 for Re(z)>1 and Im(z)=0.

Thank you, now I don't feel so dumb. The first few posts seemed to dismiss this as something trivial that I should've known since third grade. I'm glad to see now that it wasn't so trivial.
Back on topic, it seems you are on the right track, I think those branches were chosen to preserve the symmetries and the relationships between asin() and acos() that we know from the real realm.
I guess all you have to do is get a list of all symmetries, and test them using the Wikipedia formula for acos().
I can easily see acos(Z)=pi/2-asin(Z) failing if you have the other branch, since the sign of the imaginary part is opposite, you'd get acos(Z)=pi/2-conj(asin(Z)).
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 Messages In This Thread ACOS logarithmic form - Claudio L. - 04-28-2016, 03:07 PM RE: ACOS logarithmic form - Claudio L. - 04-28-2016, 03:29 PM RE: ACOS logarithmic form - Claudio L. - 04-28-2016, 05:03 PM RE: ACOS logarithmic form - Dieter - 04-28-2016, 06:44 PM RE: ACOS logarithmic form - Claudio L. - 04-28-2016, 08:23 PM RE: ACOS logarithmic form - Csaba Tizedes - 04-29-2016, 01:33 PM RE: ACOS logarithmic form - Ángel Martin - 04-28-2016, 06:42 PM RE: ACOS logarithmic form - Claudio L. - 04-28-2016, 08:29 PM RE: ACOS logarithmic form - Ángel Martin - 04-29-2016, 06:06 AM RE: ACOS logarithmic form - Claudio L. - 04-29-2016, 02:39 PM RE: ACOS logarithmic form - Valentin Albillo - 04-28-2016, 08:58 PM RE: ACOS logarithmic form - Claudio L. - 04-29-2016, 02:19 AM RE: ACOS logarithmic form - Sylvain Cote - 04-29-2016, 02:50 AM RE: ACOS logarithmic form - Ángel Martin - 04-29-2016, 06:00 AM RE: ACOS logarithmic form - ljubo - 04-29-2016, 09:15 PM RE: ACOS logarithmic form - Ángel Martin - 04-30-2016, 07:01 AM RE: ACOS logarithmic form - ljubo - 04-30-2016, 08:57 AM RE: ACOS logarithmic form - Claudio L. - 05-01-2016 03:58 AM

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