Question

se sec x = 3 e tg x < 0 então sen x vale​

Answer 1

$\Large\boxed{\begin{array}{l}\sf sec(x)=3\\\sf 1+tg^2(x)=sec^2(x)\\\sf 1+tg^2(x)=3^2\\\sf 1+tg^2(x)=9\\\sf tg^2(x)=9-1\\\sf tg^2(x)=8\\\sf tg(x)=-\sqrt{8}\\\sf tg(x)=-\sqrt{2^2\cdot2}\\\sf tg(x)=-2\sqrt{2}\end{array}}$

$\Large\boxed{\begin{array}{l}\sf sec(x)=3\implies cos(x)=\dfrac{1}{3}\\\sf tg(x)=\dfrac{sen(x)}{cos(x)}\\\\\sf sen(x)=cos(x)\cdot tg(x)\\\\\sf sen(x)=\dfrac{1}{3}\cdot-2\sqrt{2}\\\\\sf sen(x)=-\dfrac{2\sqrt{2}}{3}\end{array}}$