Question

determine o valor do cosx sabendo que 2 seno x + 3 cos x= 0

Answer 1

$2.sen(x)+3.cos(x)=0$ =>
$2.sen(x)=-3.cos(x)$ =>
$\frac{sen(x)}{cos(x)}=-\frac{3}{2}$ =>
$tg(x)=-\frac{3}{2}$.

$sec^2(x)=1+tg^2(x)$ =>
$sec^2(x)=1+\frac{9}{4}$ =>
$sec^2(x)=\frac{4}{4}+\frac{9}{4}$ =>
$sec^2(x)=\frac{13}{4}$ =>
$sec(x)=\sqrt{\frac{13}{4}}$ =>
$sec(x)=\frac{\sqrt{13}}{2}$.

$sec(x)=\frac{1}{cos(x)}$ =>
$cos(x)=\frac{2}{\sqrt{13}}$ =>
$cos(x)=\frac{2\sqrt{13}}{13}$.