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How do you convert a polar line to a line in standard form? That being, change a line with parameters rho and theta in a polar coordinate system, to a standard form (Ax+By=C) in Cartesian coordinates?

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You mean like this? analyzemath.com/polarcoordinates/polar_to_rectangular_eq.html –  Amzoti Sep 24 '12 at 4:38
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A straight line or something more general? –  Henry Sep 24 '12 at 7:15
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up vote 1 down vote accepted

In even more general cases than converting a line to and from polar, you can use the substitutions $$r=\sqrt{x^2+y^2}, \theta=\arctan(y/x), x=r\cos\theta, y=r\sin\theta$$ Note that because $\arctan$ only takes values in $(-\pi/2,\pi/2)$, the identity given for $\theta$ doesn't do all the work: you need to decide between the fourth and the second, and between the first and the third, quadrants based on the signs of $x$ and $y$.

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