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ACOS logarithmic form
04-28-2016, 05:03 PM (This post was last modified: 04-28-2016 05:04 PM by Claudio L..)
Post: #3
RE: ACOS logarithmic form
Sorry if I turned this into a monologue, but I'll leave it written for the curious reader.
So how's the 50g and everybody else doing it?

It seems everybody has a slightly different formula for ACOS, but everybody agrees 100% identical for ASIN.
ASIN doesn't have a problem, whether you use the calculator, or do it "by hand" following the formula you get the same result.

Here, all the way to the bottom, we have a formula from Mathworks.
And here is the implementation from Wolfram.

Basically, Wolfram just does pi/2-asin(Z), so the branch chosen is consistent with the ASIN results.
Mathworks uses a formula slightly different from Wikipedia:

Wikipedia uses sqrt(Z^2-1), while the other formula has i*sqrt(1-Z^2).

Before somebody jumps and says "it's the same!", let's try a couple of cases:

Z=2:
sqrt(2^2-1)=1.73...
i*sqrt(1-2^2)=i*sqrt(-3) = i*(i*1.73...) = -1.73...

Z=2+3*i:
sqrt(Z^2-1)=sqrt(-6+12*i)=(1.92...,3.11...)
i*sqrt(1-Z^2)=sqrt(6-12*i)=i*(3.11...,-1.92...)=(1.92..., 3.11...)

Z=2-3*i:
sqrt(Z^2-1)=sqrt(-6-12*i)=(1.92...,-3.11...)
i*sqrt(1-Z^2)=sqrt(6+12*i)=i*(3.11...,1.92...)=(-1.92..., 3.11...)

Very subtle... the second form gives results consistent with the 50g for all values.
It would never occur to me that such a trivial expression manipulation would push you through a different solution. Very sneaky.
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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 - 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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