Question

Alguém?Dados sen x = −3/4 e cos x = −√74, com π < x < 3π/2, calcule tg(x)

Answer 1

$tg(x) = \frac{sen(x)}{cos(x)}$

$tg(x)= \frac{ -\frac{3}{4} }{ - \sqrt{74} } = \frac{3}{4 \sqrt{74} } . \frac{ \sqrt{74} }{ \sqrt{74} } = \frac{3 \sqrt{74} }{296}$

Já que x está no terceiro quadrante ela continuará sendo positiva.

Answer 2

$\text{sen}\,=-\dfrac{3}{4}\qquad\qquad\qquad\cos{x}=-\sqrt{74}\\\\\\\\\text{tg}{x}=\dfrac{\text{sen}\,x}{\cos{x}}\\\\\\\text{tg}\,x=\dfrac{-\dfrac{3}{4}}{-\sqrt{74}}\longrightarrow\text{tg}\,{x}=\dfrac{-\dfrac{3}{4}}{-\sqrt{74}}\cdot\dfrac{-\sqrt{74}}{-\sqrt{74}}\longrightarrow\text{tg}\,{x}=\dfrac{\dfrac{3\sqrt{74}}{4}}{\sqrt{74\cdot74}}\longrightarrow$


$\text{tg}\,x=\dfrac{\dfrac{3\sqrt{74}}{4}}{\sqrt{74^2}}\longrightarrow\text{tg}\,x=\dfrac{\dfrac{3\sqrt{74}}{4}}{74}\longrightarrow\text{tg}\,x=\dfrac{3\sqrt{74}}{4}\cdot\dfrac{1}{74}\longrightarrow\\\\\\\boxed{\text{tg}\,x=\dfrac{3\sqrt{74}}{296}}$