Question

As coordenadas polares do ponto P=(x,y)=(0,-4) são:
a) (4, 3r/2)
b) (1/2, 3r/2)
c) (4, r/2)
d) (2,r/3)
e) (2,r/4)

Answer 1

$x = r*cos(\theta)\\\\y = r*sen(\theta)\\\\r = \sqrt{x^2+y^2}\\\\ \theta = arctg( \frac{y}{x} )$

convertendo
P(0,-4)
$r= \sqrt{0^2+(-4^2)} \\\\r=4$
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$x = r*cos(theta)\\\\0=4*cos(\theta)\\\\ \frac{0}{4}= cos(\theta) \\\\ 0 = cos(\theta)\\\\ arcos(0) = \theta\\\\ 90^\circ=0\\\\ \frac{\pi}{2}= \theta$
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em coordenadas polares fica
$P(r;\theta)\\\\p(4; \frac{\pi}{2} )$