Question

Sendo sen x = (-1)/2 e cos x = (- √3)/2 , no terceiro quadrante, calcular cotg x

Answer 1

Vamos relembrar que :

$\displaystyle Cotg(x) = \frac{1}{Tg(x)}$

e :

$\displaystyle Tg(x) = \frac{Sen(x)}{Cos(x)}$.

Então :

$\displaystyle Cotg(x) = \frac{1}{\frac{sen(x)}{cos(x)}} \to \fbox{\displaystyle Cotg(x) = \frac{Cos(x)}{Sen(x)} }$

A questão pede a Cotg(x) e nos informa que :

$\displaystyle Sen(x)= \frac{-1}{2}$ , $\displaystyle Cos(x) = \frac{-\sqrt{3}}{2}$

Portanto :

$\displaystyle Cotg(x) = \frac{\displaystyle \frac{-\sqrt{3}}{2}}{\displaystyle \frac{-1}{2}}$

$\fbox{\displaystyle Cotg(x) = \sqrt{3} }$