Question

Se Sen(x) = - 1/3 e sabendo que 180º < x < 270º . O valor de Sec(x), é: Obs.: lembrar de simplificar a raiz.

a) 3√2 / 4
b) 2√8 / 3
c) -3√2 / 4
d) -2√8 / 3
e) NDA ( Nenhuma das alternativas)​

Answer 1

$\Large\boxed{\begin{array}{l}\sf sen(x)=-\dfrac{1}{3}\implies sen^2(x)=\dfrac{1}{9}\\\\\sf cos^2(x)=\dfrac{9}{9}-\dfrac{1}{9}=\dfrac{8}{9}\\\\\sf cos(x)=-\sqrt{\dfrac{8}{9}}=-\dfrac{2\sqrt{2}}{3}\\\\\sf sec(x)=-\dfrac{3}{2\sqrt{2}}=-\dfrac{3\sqrt{2}}{4}\\\\\huge\boxed{\boxed{\boxed{\boxed{\sf\maltese~alternativa~c}}}}\end{array}}$