A tg(x) é dada pelo quociente entre sen(x) e cos(x).
[tex]\boxed{tg(x)~=~\dfrac{sen(x)}{cos(x)}}[/tex]
Substituindo o valor de sen(x) e cos(x), dados no enunciado, temos:
[tex]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}}[/tex]
Racionalizando a fração obtida para tg(x):
[tex]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[/tex]
[tex]\Huge{\begin{array}{c}\Delta \tt{\!\!\!\!\!\!\,\,o}\!\!\!\!\!\!\!\!\:\,\perp\end{array}}Qualquer~d\acute{u}vida,~deixe~ um~coment\acute{a}rio[/tex]
