How do you convert $(0, -6)$ to polar form?

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Answer 1 · 2016-06-29T17:26:43

Polar coordinates are $(6,-pi/2)$ .

When Cartesian coordinates $(x,y)$ are converted into polar coordinates $(r,theta)$ , we have the relation

$x=rcostheta$ and $y=rsintheta$ and hence

$r=sqrt(x^2+y^2)$ , $costheta=x/r$ and $sintheta=y/r$ .

hence for $(0,-6)$

$r=sqrt(0^2+(-6)^2)=sqrt(0+36)=sqrt36=6$

and as $costheta=0/6=0$ and $sintheta=-6/6=-1$ ,

we have $theta=-pi/2$

Hence polar coordinates are $(6,-pi/2)$ .

Answer 2 · 2016-06-29T17:40:57

Polar conversion is $(6,-pi/2).$

Cartesian $(x,y)$ in polar is $(r,theta)$ , where, $x=rcostheta, y=rsintheta, theta in(-pi,pi], x^2+y^2=r^2.$

Clearly, $r=6.$

Now $x=rcostheta rArr 0=6costheta rArr costheta = 0.$
$y=rsintheta rArr -6=6sintheta rArr sintheta =-1.$

We conclude that $theta=-pi/2.$

Hence, polar conversion is $(6,-pi/2).$

How do you convert (0, -6)(0, -6) to polar form?