Question

Assinale a alternativa que corresponde a uma representação em coordenada polar do ponto (4√2, -4√2):
a) P(6, 7pi/4)
b) P(4, 7pi/4)
c) P(8, pi/4)
d) P(4, -7pi/4)
e) P(8, -pi/4)

Answer 1

Boa noite Danado!

Vamos ter que determinar o ângulo teta usando uma relação trigonométrica no triângulo retângulo.

$Tag\theta= \dfrac{Cateto~~oposto}{Cateto~~adjacente}\\\\\\ Tag\theta= \dfrac{-4 \sqrt{2} }{~~4 \sqrt{2} }\\\\\\ Tag\theta=-1\\\\\\ Ent\~ao~a~~tangente~e~de~315\º,escrevendo~ ela~ em radianos~fica~assim.$

$\theta= \dfrac{315}{180}\\\\\\ \theta= \dfrac{315 \pi }{180}\\\\\\ Simplificando~~por~~45!\\\\\\ \theta= \dfrac{315:45 \pi }{180:45}\\\\\\ \boxed{\theta= \dfrac{7\pi }{4}}$


$x=rsen\theta\\\\\\\ x=(4 \sqrt{2}).( \frac{ \sqrt{2} }{2} )\\\\\\\ x=(4 \sqrt{2}).( \frac{ \sqrt{2} }{2} )\\\\\\\ x= (2 \sqrt{2}. \sqrt{2})\\\\\\\ x= (2 \sqrt{4})\\\\\\\ x=2.2\\\\\ \boxed{x=4}$


$\boxed{Resposta:~~\bigg(2, \frac{7 \pi }{4}\bigg)~~\boxed{Alternativa~~B}}$

Boa noite!
Bons estudos!