Arctan or Arccos?
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Arctan or Arccos?

 
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Real_McCoy
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Posted: Sat Dec 03, 2005 1:16 am    Post subject: Arctan or Arccos? Reply with quote
I remember a mathematician saying to me a while back that engineers always
work out phase using arctan (img/real).

He went on to say that this was not a good method due to problems with
quadrants etc. Far better to use arccos
arccos(real/abs) if my sums are right.

McC
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Tim Wescott
Guest
Posted: Sat Dec 03, 2005 1:16 am    Post subject: Re: Arctan or Arccos? Reply with quote
Real_McCoy wrote:
Quote:
I remember a mathematician saying to me a while back that engineers always
work out phase using arctan (img/real).

He went on to say that this was not a good method due to problems with
quadrants etc. Far better to use arccos
arccos(real/abs) if my sums are right.

McC


Either one leads to ambiguities.


If you're going to obtain an angle directly using trig functions you
want to use something like atan2 in the C library, which takes two
arguments.

In the guts of the thing it finds the quadrant based on the relative
absolute values and the signs of the numbers, then it takes theta =
arctan(x) where |x| is always less than 1, then it flips and offsets
theta to put it in the correct quadrant.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com
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robert bristow-johnson
Guest
Posted: Sat Dec 03, 2005 1:16 am    Post subject: Re: Arctan or Arccos? Reply with quote
Tim Wescott wrote:
Quote:
Real_McCoy wrote:
I remember a mathematician saying to me a while back that engineers always
work out phase using arctan (img/real).

He went on to say that this was not a good method due to problems with
quadrants etc. Far better to use arccos(real/abs) if my sums are right.

Either one leads to ambiguities.

perhaps that mathematician was thinking of this:

Arg(z) = sgn( Im(z) ) * Arccos( Re(z) / |z| )

that works for all 4 quadrants and gives you the principle value of
arg() but of course has some numerical problems for the case where z is
real.

r b-j
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