Question

Calculati cosx stiind ca sinx=1/3 si x apartine (0, π/2)

Answer 1

$x\in(0, \frac{\pi}{2}) \\ \\ sinx= \frac{1}{3} \\ sin^{2}x+ cos^{2}x = 1 \Rightarrow cos^{2}x=1-sin^{2}x\Rightarrow cos^{2}x = 1 - \frac{1}{9} \Rightarrow \\ \Rightarrow cos^{2}x = \frac{8}{9} \Rightarrow cosx= \pm\frac{2 \sqrt{2} }{3} \\ Dar\quad x\in(0, \frac{\pi}{2}) \Rightarrow cosx = \frac{2 \sqrt{2} }{3}$