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 :

\(\sin \dfrac {5\pi}{12} = \dfrac {\sqrt 6 + \sqrt 2} 4\)