Question #47750

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Answer 1 · 2016-12-09T07:25:44

The polar equation is $r = 2$ $r=2$

To convert from rectangular coordinates $(x, y)$ $(x,y)$ to polar coordinates $(r, θ)$ $(r,theta)$ , we use the following equations

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$

The equation is

$x^{2} + y^{2} = 4$ $x^2+y^2=4$

$r^{2} {cos}^{2} θ + r^{2} {sin}^{2} θ = 4$ $r^2cos^2theta+r^2sin^2theta=4$

$r^{2} ({cos}^{2} θ + {sin}^{2} θ) = 4$ $r^2(cos^2theta+sin^2theta)=4$

As, ${cos}^{2} θ + {sin}^{2} θ = 1$ $cos^2theta+sin^2theta=1$

The equation becomes

$r^{2} = 4$ $r^2=4$

$r = 2$ $r=2$

We take only the positive value.