Question
Calculer \(\cos \dfrac {5\pi}{12}\)
Indice
On pourra remarquer que \(\dfrac{5\pi}{12} = \dfrac \pi 4 + \dfrac \pi 6\)
Solution
\(\cos \dfrac {5\pi}{12} = \cos \left( \dfrac \pi 4 + \dfrac \pi 6\right)\)
\(\cos \dfrac {5\pi}{12} = \cos \dfrac \pi 4 \cos \dfrac \pi 6 - \sin \dfrac \pi 4 \sin\dfrac \pi 6\)
\(\cos \dfrac {5\pi}{12} = \dfrac {\sqrt 2} 2 \dfrac {\sqrt 3} 2 - \dfrac {\sqrt 2} 2 \dfrac 1 2\)
\(\cos \dfrac {5\pi}{12} = \dfrac {\sqrt 6 - \sqrt 2} 4\)
Question
Calculer \(\sin \dfrac {5\pi}{12}\)
Solution
On procède de même que ci-dessus :
\(\sin \dfrac {5\pi}{12} = \dfrac {\sqrt 6 + \sqrt 2} 4\)