Question

Calculati cos x ,stiind ca sin x =2/3, x apartine (0, pi/2)

Answer 1

[tex]\sin^2 x+\cos ^2 x=1\\ \cos ^2x =1-\sin^2 x\\ \cos ^2 x=1-\dfrac{4}{9}\\ \cos^2 x=\dfrac{5}{9}\\ \cos x=\pm \dfrac{\sqrt5}{3}\\ x\in\left(0,\dfrac{\pi}{2}\right)\Rightarrow \boxed{\cos x=\dfrac{\sqrt 5}{3}}[/tex]