How do you find the polar coordinates given the rectangular coordinates (2,-2)?

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Answer 1 · 2016-12-23T15:46:59

The answer is $=(2sqrt2, -pi/4)$

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

$x=rcostheta$

$y=rsintheta$

and $r=sqrt(x^2+y^2)$

Here, $(x,y)$ is $(2,-2)$

$r=sqrt(4+4)0sqrt8=2sqrt2$

$costheta=2/(2sqrt2)=sqrt2/2$

$sintheta=-2/(2sqrt2)=-sqrt2/2$

For these values of $costheta$ and $sintheta$ , we are in quadrant IV

$:.theta=-pi/4$

The polar coordinates are $(2sqrt2, -pi/4)$