Question

Psendo senX=1/4 e π/2<X<π, calcule cos (x- π/3)

Answer 1

$<var>cos(x - \frac{\pi}{3})=cosx\cdot cos(\frac{\pi}{3})+senx\cdot sen(\frac{\pi}{3})</var>$

$<var>cos(x - \frac{\pi}{3})=\frac{-\sqrt{15}}{4} \cdot \frac{1}{2}+ \frac{\sqrt3}{2} \cdot \frac{1}{4}=\frac{\sqrt {3}-\sqrt{15}}{8}</var>$

 

 

O cos x deve ser obtido da expressão:

 

$<var>cos x=\sqrt{1-sen^2 x}=-\frac{\sqrt{15}}{4}</var>$