Question

determine x, em radiano, sabendo que tg( x + π/2)= -√3​

Answer 1

Resposta:

$S=\{x=\frac{\pi }{6} +k\pi ,~k\in Z\}$

Explicação passo a passo:

$tg(x+\frac{\pi }{2})=-\sqrt{3}$

$x+\frac{\pi }{2} \in~~2\°~q\implies~tg <0\\\\tg(x+\frac{\pi }{2})=-tg(\pi-(x+\frac{\pi }{2})=-tg(\frac{\pi }{2}-x)=-cotgx$

$-cotgx=-\sqrt{3} \\\\cotgx=\sqrt{3} \\\\tgx=\frac{1}{\sqrt{3} } \\\\tgx=\frac{\sqrt{3} }{3}$

$S=\{x=\frac{\pi }{6} +k\pi ,~k\in Z\}$