Question

Resolver a inequação 2sen x+√3<0

Answer 1

Explicação passo-a-passo:

$\sf 2\cdot sen~x+\sqrt{3} < 0$

$\sf 2\cdot sen~x < -\sqrt{3}$

$\sf sen~x < \dfrac{-\sqrt{3}}{2}$

Nos dois primeiros quadrantes, o seno é positivo

Temos que:

$\sf sen~240^{\circ}=\dfrac{-\sqrt{3}}{2}~\Rightarrow~sen~\Big(\dfrac{4\pi}{3}\Big)=\dfrac{-\sqrt{3}}{2}$

$\sf sen~300^{\circ}=\dfrac{-\sqrt{3}}{2}~\Rightarrow~sen~\Big(\dfrac{5\pi}{3}\Big)=\dfrac{-\sqrt{3}}{2}$

Logo:

$\sf \red{S=\Big\{\dfrac{4\pi}{3};~\dfrac{5\pi}{3}\Big\}}$

Letra A