Question

Sendo sen x = 1/3 com 0 < X < /2, calcule o valor de cos x .

Answer 1

$\sin{x}=\dfrac{1}{3}$

$\boxed{\sin^2{x}+\cos^2{x}=1}\ \therefore$

$\bigg(\dfrac{1}{3}\bigg)^2+\cos^2{x}=1\ \therefore\ \cos^2{x}=\dfrac{9}{9}-\dfrac{1}{9}\ \therefore$

$\cos^2{x}=\dfrac{8}{9}\ \therefore\ \cos{x}=\sqrt{\dfrac{2^2(2)}{3^2}}\ \therefore\ \boxed{\cos{x}=\pm\dfrac{2\sqrt{2}}{3}}$

$\text{Como}\ 0\leq x\leq\dfrac{\pi}{2}\ \to\ \cos{x}\geq0.\ \text{Logo:}$

$\boxed{\cos{x}=\dfrac{2\sqrt{2}}{3}}$