Question

Resolva a equação trigonométrica:  [0;2π]

tg²x = 1/3

Answer 1

$tg ^{2}x= \frac{1}{3}$

$tg^{^{}}x= \sqrt{ \frac{1}{3} }$  or  $tg^{^{}}x= -\sqrt{ \frac{1}{3} }$

$tg^{^{}}x= \frac{1}{3} \sqrt{3}$ or $tg^{^{}}x= -\frac{1}{3} \sqrt{3}$

$tg^{^{}}x= tg^{^{}}30$          or    $tg^{^{}}x= tg^{^{}}150$
             $tg^{^{}}210$                             $tg^{^{}}330$

x= 30⁰ = $\frac{30}{180} \pi = \frac{1}{6} \pi$

x= 150⁰ = $\frac{150}{180} \pi = \frac{5}{6} \pi$

x= 210°= $\frac{210}{180} \pi = \frac{7}{6} \pi$

x= 330°=$\frac{330}{180} \pi = \frac{11}{6} \pi$

S { $\frac{ \pi }{6}, \frac{5 \pi }{6}, \frac{7 \pi }{6}, \frac{11 \pi }{6}$}