Question

Sendo sen α =-1/3 e α ∈ 4 quadrante calcule cos α e tg α ?
POR FAVOR RÁPIDO!!!!!!!!!!!!!

Answer 1

$\sin^2 \alpha +\cos^2 \alpha=1\\\\\\\left(-\dfrac13 \right)^2+\cos^2\alpha=1\\\\\dfrac19+\cos^2\alpha=1\\\\\cos^2\alpha=\dfrac89\\\\\cos\alpha=\pm\sqrt{\dfrac89}=\pm\dfrac{2\sqrt2}{3}$


Como α se encontra no quarto quadrante cosseno eh positivo, entao desses dois resultados considere apenas o positivo.
 Agora pra tangente eh soh dividir o seno pelo cosseno:

$\tan \alpha=\dfrac{\sin \alpha}{\cos\alpha}=\dfrac{-\frac13}{\frac{2\sqrt2}{3}}=-\dfrac{1}{2\sqrt2}=-\dfrac{\sqrt{2}}{4}$