Question

DADO SEN X = 3/4 E COS X = −√7 /4, CALCULE TG X :

Answer 1

A tg(x) é dada pelo quociente entre sen(x) e cos(x).

$\boxed{tg(x)~=~\dfrac{sen(x)}{cos(x)}}$

Substituindo o valor de sen(x) e cos(x), dados no enunciado, temos:

$tg(x)~=~\dfrac{\dfrac{3}{4}}{-\dfrac{\sqrt{7}}{4}}\\\\\\tg(x)~=~\dfrac{3}{4}~\cdot~\left(- \dfrac{4}{\sqrt{7}}\right)\\\\\\tg(x)~=~\dfrac{3}{4\!\!\!\backslash}~\cdot~\left(- \dfrac{4\!\!\!\backslash}{\sqrt{7}}\right)\\\\\\tg(x)~=~- \dfrac{3}{\sqrt{7}}$

Racionalizando a fração obtida para tg(x):

$tg(x)~=~-\dfrac{3}{\sqrt{7}}~\cdot ~\dfrac{\sqrt{7}}{\sqrt{7}}\\\\\\tg(x)~=~-\dfrac{3\cdot \sqrt{7}}{\sqrt{7}^{\,2}}\\\\\\\boxed{tg(x)~=~-\dfrac{3\sqrt{7}}{7}}~~ \Rightarrow~Resposta$

$\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio$