Question

Resolva a equação e a inequação , talque 0 ≤ x < 2π:
a) tg^2 x = 3
b) tg x < √3/3

Answer 1

a)

$\sf{tg^2(x)=3}\\\sf{tg(x)=\pm\sqrt{3}}$

$\sf{tg(x)=\sqrt{3}}\\\sf{x=\dfrac{\pi}{3}~~ou~~x=\dfrac{4\pi}{3}}\\\sf{tg(x)=-\sqrt{3}}\\\sf{x=\dfrac{2\pi}{3}~~ou~~x=\dfrac{5\pi}{3}}\\\large\boxed{\boxed{\boxed{\boxed{\sf{S=\{\dfrac{\pi}{3},\dfrac{4\pi}{3},\dfrac{2\pi}{3},\dfrac{5\pi}{3}\}}}}}}$

b)

$\sf{tg(x)\textless\dfrac{\sqrt{3}}{3}}\\\sf{0\leq x\leq\dfrac{\pi}{6}~~ou~~\pi\leq x\leq\dfrac{7\pi}{6}}$