>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.
I'll continue this conversation a bit longer, but I have professoring to get back to starting next week, with new thesis students to get up to speed, classes to teach, research deadlines, etc.
You seem to continue to not understand. I do not "want" an asin2 function. My contention is that it is impossible and that one is stuck with the principal value of the inverse sine function. You agree with me but you keep talking around the issue.
Let me tell you one more time: I do not want a _unique_ value for asin2(1,sqrt(2)) to have. My point (and yours) is that it cannot tell the difference between pi/4 and 3*pi/4.
It occurs to me that you are putting me on and are not as dense as you seem. But I'm new to this newsgroup and will soon leave it.
I'll try to summarize all this in my response to Virgil.
>> 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.
I do fully understand what atan2 was designed to do, as I have explained in delineating the contrast with a potential asin2, your patronizing comment notwithstanding.
I assumed readers in this newsgroup were familiar with the function atan2, but perhaps that is not so.
>> 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.
They can indeed be interpreted that way if you are teaching or taking a high school trigonometry class. But in general tan(t) = sin(t)/cos(t) = u/v, and t = atan2(u,v). As an example, one can determine the tangent of the optimal angle for a rocket thrust as the ratio of certain adjoint variables that appear in the optimization problem.
>> 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.
That is exactly my point. You agree with me, but continue to argue about points we agree on. And you say above that u and v can be interpreted as Cartesian coordinates of a point in the plane.
Perhaps you enjoy this trolling, but it doesn't serve this newsgroup nor Sigma Xi very well.
Are you really on the staff of Sigma Xi? I'll look for you on their national web page. And all these years I've been paying dues. Fortunately, American Scientist is an interesting magazine.
> David Cantrell
>Sent via Deja.com http://www.deja.com/ >Before you buy. -- =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= John E. Prussing Dept. of Aeronautical & Astronautical Engineering University of Illinois at Urbana-Champaign http://www.uiuc.edu/~prussing =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=