Question

Sa se calculeze cos ( (7 *pi)/12).Va rog sa fie rezolvat detaliat (nu am înțeles la ora cum se rezolva acest tip de exercitiu)

Answer 1

Salut,

Știm că cos(a + b) = cosa·cosb -- sina·sinb.

$cos\left(\dfrac{7\pi}{12}\right)=cos\left(\dfrac{4\pi+3\pi}{12}\right)=cos\left(\dfrac{4\pi}{12}+\dfrac{3\pi}{12}\right)=\\\\=cos\left(\dfrac{\pi}{3}+\dfrac{\pi}{4}\right)=cos\left(\dfrac{\pi}{3}\right)\cdot cos\left(\dfrac{\pi}{4}\right)-sin\left(\dfrac{\pi}{3}\right)\cdot sin\left(\dfrac{\pi}{4}\right)=\\\\=\dfrac{1}{2}\cdot\dfrac{\sqrt2}{2}-\dfrac{\sqrt3}{2}\cdot\dfrac{\sqrt2}{2}=\dfrac1{4}(\sqrt2-\sqrt6).\ A\ fost\ greu\ ?$

Green eyes.