« Valeurs trigonométriques exactes » : différence entre les versions

Contenu supprimé Contenu ajouté
m Insertion de cosinus, sinus et tangente de 3°
m 21° et 33°
Ligne 36 :
| align="center" | <math>\frac{\sqrt{10-2\sqrt5}+\sqrt3+\sqrt{15}}8</math>
| align="center" | <math>\frac{\sqrt{30-6\sqrt5}-\sqrt5-1}8</math>
| align="center" | <math>\frac12frac{ \left(sqrt{2} \sqrt{105-2\sqrt5}-\sqrt{153}+(\sqrt3\rightsqrt{5}-1)}{2}</math>
|-
| scope="row" | <math>\frac\pi{24}</math>
Ligne 46 :
| scope="row" | <math>\frac\pi{20}</math>
| align="center" | 9°
| align="center" | <math>\frac{\sqrt28sqrt2\left(1+\sqrt5 +1\right)+ 2\sqrt{105-2\sqrt5}\right)}{8}</math>
| align="center" | <math>\frac{\sqrt28sqrt2 \left(1+\sqrt5 +1\right)-2\sqrt{105-2\sqrt5}\right)}{8}</math>
| align="center" | <math>\sqrt5+1-\sqrt{5+2\sqrt5}</math>
|-
Ligne 58 :
| scope="row" | <math>\frac\pi{15}</math>
| align="center" | 12°
| align="center" | <math>\frac{\sqrt{30+6} \sqrt{5+\sqrt5}+\sqrt5-1}8</math>
| align="center" | <math>\frac{ \sqrt{10+2} \sqrt{5+\sqrt5}+-\sqrt3-(\sqrt{155}-1)}8</math>
| align="center" | <math>\frac{3\sqrt3 (3-\sqrt{155})-\sqrt{502} \sqrt{25-2211\sqrt5}}2</math>
|-
| scope="row" | <math>\frac\pi{12}</math>
Ligne 76 :
| scope="row" | <math>\frac\pi{10}</math>
| align="center" | 18°
| align="center" | <math>\frac{\sqrt{10+2}\sqrt{5+\sqrt5}}{4}</math>
| align="center" | <math>\frac{\sqrt5-1}4</math>
| align="center" | <math>\frac{\sqrt{15}\sqrt{5-\frac252\sqrt5}}{5}</math>
|-
|<math>\frac{7 \pi}{60}</math>
|21°
|<math>\frac{2(\sqrt{3}-1)\sqrt{5-\sqrt{5}} +\sqrt{2}(\sqrt{3}+1)(\sqrt{5}+1)}{16}</math>
|<math>\frac{2(\sqrt{3}+1)\sqrt{5-\sqrt{5}} -\sqrt{2}(\sqrt{3}-1)(\sqrt{5}+1)}{16}</math>
|<math>\frac{\left( 2-(2+\sqrt{3})(3-\sqrt{5})\right) \left(2-\sqrt{2} \sqrt{5+\sqrt{5}} \right)}{4}</math>
|-
| scope="row" | <math>\frac\pi8</math>
Ligne 88 ⟶ 94 :
| scope="row" | <math>\frac{2\pi}{15}</math>
| align="center" | 24°
| align="center" | <math>\frac{\sqrt5+1 + \sqrt{30-6\sqrt5}+\sqrt{5-\sqrt5+1}}8</math>
| align="center" | <math>\frac{\sqrt3(\sqrt{105}+1)-2\sqrt5sqrt{2}-\sqrt3- \sqrt{155-\sqrt5}}8</math>
| align="center" | <math>\frac{-3\sqrt3-\sqrt{152}+ \sqrt{5025+2211\sqrt5}-\sqrt3(3+\sqrt{5})}2</math>
|-
| scope="row" | <math>\frac{3\pi}{20}</math>
| align="center" | 27°
| align="center" | <math>\frac{2\sqrt28\left(1-sqrt{5+\sqrt5-} +\sqrt{10+2}\left(\sqrt5}-1\right) }{8}</math>
| align="center" | <math>\frac\sqrt28\left(1-\sqrt5+{2\sqrt{105+2\sqrt5} -\sqrt2\left(\sqrt5-1\right)}{8}</math>
| align="center" | <math>\sqrt5-1-\sqrt{5-2\sqrt5}</math>
|-
Ligne 109 ⟶ 115 :
| align="center" | <math>\frac12</math>
| align="center" | <math>\frac\sqrt33</math>
|-
|<math>\frac{11\pi}{60}</math>
|33°
|<math>\frac{2(\sqrt{3}+1)\sqrt{5+\sqrt{5}}-\sqrt{2}(\sqrt{3}-1)(\sqrt{5}-1)}{16}</math>
|<math>\frac{2(\sqrt{3}-1)\sqrt{5+\sqrt{5}}+\sqrt{2}(\sqrt{3}+1)(\sqrt{5}-1)}{16}</math>
|<math>\frac{\left(2-(2-\sqrt{3})(3+\sqrt{5}) \right) \left(2+\sqrt{2} \sqrt{5-\sqrt{5}} \right)}{4}</math>
|-
| scope="row" | <math>\frac{3\pi}{16}</math>