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)#