Question

seja um arco x no terceiro quadrante e sua secante vale -2 calcule tg x

Answer 1

$sec(x)=\frac{1}{cos(x)} \\ \\ -2=\frac{1}{cosx} \\ \\ cos(x)=-\frac{1}{2}$

$sen(x)=\sqrt{1-cos^2x} \\ \\ sen(x)=\sqrt{1-(-\frac{1}{2})^2} \\ \\ sen(x)=\sqrt{1-\frac{1}{4}} \\ \\ sen(x)=\sqrt{\frac{3}{4}} \\ \\ sen(x)=\frac{\sqrt3}{2}$

$\boxed{tg(x)=\frac{sen(x)}{cos(x)}=\frac{\frac{\sqrt3}{2}}{-\frac{1}{2}}=\sqrt3}$