How do you convert $y = -x$ into polar form?

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Answer 1 · 2016-06-10T05:14:43

Polar form of $y=-x$ is $theta=(3pi)/4$

The relation between polar coordinates $(r,theta)$ and Cartesian coordinates $(x,y)$ is given by

$x=rcostheta$ , $y=rsintheta$ and $r^2=x^2+y^2$

As such $y=-x$ can be written as

$rsintheta=-rcostheta$ or

$(rsintheta)/(rcostheta)=-1$ or

$tantheta=-1=tan((3pi)/4)$ or

$theta=(3pi)/4$

How do you convert y = -xy = -x into polar form?