How do you change the rectangular equation $x-sqrt3y=0$ into polar form?

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Answer 1 · 2016-08-10T15:30:53

A line passing by the origin with declivity

$theta = arctan(sqrt(3)/3)$

From the pass equations

${ (x = r cos(theta)), (y=r sin(theta)) :}$

we have

$r cos(theta)-sqrt3r sin(theta)=r(cos(theta)-sqrt(3) sin(theta))=0$

For any $r$ we have

$tan(theta) = sqrt(3)/3$ which represents the line passing by the origin with declivity $theta = arctan(sqrt(3)/3)$

How do you change the rectangular equation x-sqrt3y=0x-sqrt3y=0 into polar form?