Question

Sabendo que $sen \alpha = \frac{3}{5}$  e $a E] \pi \frac{ \pi }{2} [$ ,determine  o valor de $tg \alpha$

Answer 1

Relação fundamental da trigonometria:

$\boxed{sen^2 \alpha+cos^2 \alpha =1} \\ \\ cos^2 \alpha = \sqrt{1-sen^2 \alpha} \\ \\ cos^2 \alpha=\sqrt{1-(\frac{3}{5})}=\sqrt{1-\frac{9}{25}}=\sqrt{\frac{16}{25}}=\frac{4}{5} \\ \\ \boxed{tg \alpha =\frac{sen \alpha}{cos \alpha}=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}}$

Como 
$\alpha \in [\pi, \frac{\pi}{2}]$

Então $\boxed{tg \alpha=-\frac{3}{4}}$