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Find the equation in polar coordinate form for a straight line through the points with polar coordinates $(4,0)$ and $(4,π/3)$.

Here's my steps:

1.Write the two points in cartesian coordinates: the two points are $(4,0)$ and $(2,4)$.

2.Find the cartesian equation of the line through $(4,0)$ and $(2,4)$: $$y=-2x+8$$

3.Replace $y$ with $rsin(ø)$ and $x$ with $rcos(ø)$.

so I get $$rsin(ø)=-2rcos(ø)+8$$ ->$$r(sin(ø)+2cos(ø))=8$$

The answer in my book is $$rsin(ø+π/3)=2√3$$

which can be written in the form of $$√3y=4√3-x$$

Can someone point out where I got wrong?

  • 2
    Your conversion of the point $(4,\pi/3)$ is wrong.2012-07-13
  • 1
    second point in cartesian coordinate is $(2,2\sqrt 3)$, not $(2,4)$.2012-07-13
  • 0
    @J.M., make that an answer.2012-07-13
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    @MvG, I'd rather that Vic figure out why avatar's answer is the correct one him/herself.2012-07-13
  • 0
    thanks for pointing it out. I'm trying to do it again.2012-07-13
  • 0
    I've got the correct answer. Thank you all :)2012-07-13

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Your Cartesian co-ordinaries are incorrect. They should be $(4,0)$ and $(2 , 2\sqrt{3})$. Sorry for the bad notation. Also you then need to use the Rsin$(θ + α)$ form to get it as the book's answer.