How do you convert the Cartesian coordinates $(-1/2, -sqrt(3)/2)$ to polar coordinates?

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Answer 1 · 2016-08-30T02:56:25

Polar coordinates of $(-1/2,-sqrt3/2)$ are $(1,(4pi)/3)$ .

The relation between Cartesian coordinates $(x,y)$ and polar coordinates $(r,theta)$ is $x=rcostheta$ and $y=rsintheta$ .

As such $r=sqrt(x^2+y^2)$ and hence for $(-1/2,-sqrt3/2)$ ,

$r=-sqrt((-1/2)^2+(-sqrt3/2)^2)=-sqrt(1/4+3/4)=sqrt1=1$

Hence $costheta=x/r=-1/2$ and $sintheta=y/r=-sqrt3/2$ .

Hence $theta$ is in third quadrant and $theta=(4pi)/3$ .

Therefore polar coordinates of $(-1/2,-sqrt3/2)$ are $(1,(4pi)/3)$ .

How do you convert the Cartesian coordinates (-1/2, -sqrt(3)/2)(-1/2, -sqrt(3)/2) to polar coordinates?