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author | David A. Madore <david@procyon> | 2012-03-15 17:51:46 +0100 |
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committer | David A. Madore <david@procyon> | 2012-03-15 17:53:27 +0100 |
commit | 6fbb29ae8e7b4913ff72bb04d1960fc7fe33bf85 (patch) | |
tree | 2e20fc74b972995afc4c7d6b5ab8db28d10a4340 /chapitres/radicaux.tex | |
parent | 2b63d2fe87d077eac73a53abb61ed02f114d03fa (diff) | |
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[radicaux] Remaniement de la formule de cos(2π/13).
Diffstat (limited to 'chapitres/radicaux.tex')
-rw-r--r-- | chapitres/radicaux.tex | 12 |
1 files changed, 9 insertions, 3 deletions
diff --git a/chapitres/radicaux.tex b/chapitres/radicaux.tex index 09abca7..23cd309 100644 --- a/chapitres/radicaux.tex +++ b/chapitres/radicaux.tex @@ -709,9 +709,15 @@ vaut $\sqrt{-11}$. On obtient finalement : \[ \begin{array}{rl} \displaystyle\cos\frac{2\pi}{13} -&\displaystyle= - \frac{1}{12} + \frac{1}{12} \, \sqrt{13} + \frac{1}{24} {\left(-1 + \sqrt{-3}\right)} \, \root3\of{-\frac{65}{2} - \frac{39}{2} \, \sqrt{-3}} -- \frac{1}{24} \, {\left(1 + \sqrt{-3}\right)} \root3\of{-\frac{65}{2} + \frac{39}{2} \, \sqrt{-3}}\\ -&\displaystyle + \frac{1}{24} {\left(1 + \sqrt{-3}\right)} \, \root6\of{-\frac{4381}{2} - \frac{195}{2} \, \sqrt{-3}} - \frac{1}{24} \, {\left(-1 + \sqrt{-3}\right)} \root6\of{-\frac{4381}{2} + \frac{195}{2} \, \sqrt{-3}}\\ +&\displaystyle= - \frac{1}{12} + \frac{1}{12} \, \sqrt{13}\\ +&\displaystyle + \frac{1}{24} \root3\of{\frac{13}{2}} +\Big( + (-1 + \sqrt{-3}) \, \root3\of{-5 - 3 \, \sqrt{-3}} ++ (-1 - \sqrt{-3}) \, \root3\of{-5 + 3 \, \sqrt{-3}} \Big)\\ +&\displaystyle + \frac{1}{24} \root6\of{\frac{13}{2}} +\Big( + (1 + \sqrt{-3}) \, \root6\of{-337 - 15 \, \sqrt{-3}} ++ (1 - \sqrt{-3}) \, \root6\of{-337 + 15 \, \sqrt{-3}} \Big)\\ \end{array} \] |