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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?

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    I've got the correct answer. Thank you all :)2012-07-13

1 Answers 1

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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.