Question

Sabendo que sencx = -6, determine tg x e sen x dadp que x pertence ao segundo quadrante.

ME AJUDA PFV

Answer 1

$\large\boxed{\begin{array}{l}\sf Sabendo\,que\,sec(x)=-6,\\\sf determine\,tg(x)\,e\,sen(x)\,dado\,que\\\sf x\,pertence\,ao\,segundo\,quadrante.\\\underline{\sf soluc_{\!\!,}\tilde ao\!:}\\\rm sec(x)=-6\longrightarrow sec^2(x)=36\\\rm tg^2(x)=sec^2(x)-1\\\rm tg^2(x)=36-1\\\rm tg^2(x)=35\\\rm tg(x)=-\sqrt{35}\\\rm cos(x)=-\dfrac{1}{6}\\\\\rm sen (x)=cos(x)\cdot tg(x)\\\rm sen(x)=\bigg(-\dfrac{1}{6}\bigg)\cdot(-\sqrt{35})\\\\\rm sen(x)=\dfrac{\sqrt{35}}{6}\end{array}}$