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ArcCos[]


Hello!

I have just come across one more example that shows how there is
room for improving Mathematica's trig functions.

With Mathematica 4:

v = Cos[ Pi/8 ] // FunctionExpand   gives   Sqrt[2 + Sqrt[2]]/2

Still, neither

ArcCos[v] // FunctionExpand   nor    ArcCos[v] // FullSimplify

give  Pi/8, as I would expect, but just

ArcSec[2/Sqrt[2 + Sqrt[2]]]

%%%%%%%%%%%%%%%

An unrelated problem: the following instructions consistently crash
my Mac Mathematica 4 kernel:

a = Root[-t + 2*#1 + 2*t^2*#1 + #1^3 & , 1];
b = D[a, t];
Solve[b == 0, t]

%%%%%%%%%%%%%%%

Best regards,

        Gianluca Gorni

-- 


 +---------------------------------+
 | Gianluca Gorni                  |
 | Universita` di Udine            |
 | Dipartimento di Matematica      |
 |   e Informatica                 |
 | via delle Scienze 208           |
 | I-33100 Udine UD                |
 | Italy                           |
 +---------------------------------+
 | Ph.: (39) 0432-558422           |
 | Fax: (39) 0432-558499           |
 | mailto:gorni at dimi.uniud.it      |
 | http://www.dimi.uniud.it/~gorni |
 +---------------------------------+




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