How do you convert the equation x+y=2x to a polar equation?

Question

Would the answer just be rsintheta=rcostheta?

Answer 1

You are on the right track. 

 

r sin(θ) =  r cos(θ)      then divide both sides by r to get

 

  sin(θ) = cos(θ)      the solution to this is θ =  pi/4  ( 45 °)

 

Straight lines passing through the origin (as is the case here)  have very simple polar equations:

  θ =  arctan(m)  where m is the slope of the line.   Here  m = 1   so θ = pi/4