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Topic: asin2?
Replies: 26   Last Post: Dec 20, 2011 2:24 PM

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David W. Cantrell

Posts: 3,395
Registered: 12/3/04
Re: asin2?
Posted: Aug 16, 2000 10:20 PM
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In article <xrGm5.1082$9N1.18474@vixen.cso.uiuc.edu>,
prussing@aae.uiuc.edu (John Prussing) wrote:
> In <B5C01FD196685CAE5@0.0.0.0> g.sande@worldnet.att.net (Gordon
Sande) writes:
>
> >In article <8ne38g$k1b$1@nnrp1.deja.com>,
> >DWCantrell@sigmaxi.org wrote:

>
> >>In article <Vmhjr-E31527.00492516082000@news.frii.com>,
> >> Virgil <Vmhjr@frii.com> wrote:

> >>>In article <BJmm5.964$9N1.16698@vixen.cso.uiuc.edu>,
> >>>prussing@aae.uiuc.edu (John Prussing) wrote:
> >>>
> >>>Something to the effect that what I have done below is impossible.

> >>
> >>What John seems to be wanting, as best I can ascertain it, is indeed
> >>impossible. On the other hand, your solution below, Virgil, is fine.

>
> >>You have given what I consider to be a correct asin2, analogous to
> >>atan2, where the two arguments of the function are the coordinates
> >>of a point (x,y).

>
> This was not the question at hand.


I supposed that what Virgil gave was not what you wanted. However, you
have never made it completely clear what you did want. As best I can
tell, you want asin2 so that, for example, asin2(sqrt(2),1) can be
either pi/4 or 3*pi/4. Of course, this is impossible if asin2 is to be
a _function_. Maybe I'm interpreting what you want incorrectly; if so,
please specify the _unique_ value which you want asin2(sqrt(2),1) to
have.

> Please see below.
>

> >There seems to be little reason to call the function which goes from
> >(x,y) to the angle the "arctangent" as opposed to the "arguement"
> >which is

>
> More likely "argument".


Of course. But, with the exception of that misspelling, everything that
Gordon said is absolutely correct.

> And the reason for calling it an arctangent I try to explain below.
>

> >the traditional complex variables name. Any of these will look at
> >the signs of x and y to pick the quadrant and then use some
> >transformation of x and y to use either arctan, arcsin or acrcos.
> >For arctan, use y/x. For
> >arcsin, use y/sqrt(x*x+y*y). etc (all subject to typos)

>
> >One can only guess that atan2 ended up as the name because y/x was
> >the simplest transformation.

>
> Apparently I have (surprisingly) confused everyone with the notation.


No, not at all. Apparently you have never understood clearly what atan2
was designed to do! And it is certainly rather silly to try to talk
about an analogous asin2 until you fully understand the purpose of
atan2.

> x and y were intended to be dummy arguments, not cartesian components
> of some point.


No, the two arguments of atan2 may indeed be considered to be the
Cartesian coordinates of some point.

> In numerical computation one typically encounters tan(t) = w to be
> solved for t, or if you are lucky tan(t) = u/v. In the latter case
> atan2 uses the fact that tan(t) = sin(t)/cos(t) to infer the
> algebraic signs of both sin(t) and cos(t) and therefore the quadrant
> of t. That doesn't work for sin(t) = u/v.
>
> I gave an example using the Law of Sines: sin(A) = a*sin(B)/b to be
> solved for A, given the values of a, B and b.
> It is of the form sin(A) = u/v.
> What does that have to do with a point in the x-y plane?


Nothing directly, just as tan(A) = u/v has nothing directly to do with
a point in the plane.

David Cantrell


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