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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? – Amzoti Sep 24 '12 at 4:38
A straight line or something more general? – Henry Sep 24 '12 at 7:15
up vote 1 down vote accepted

In even more general cases than converting a line to and from polar, you can use the substitutions $$r=\sqrt{x^2+y^2}, \theta=\tan^{-1}\left(\frac{y}{x}\right), x=r\cos\theta, y=r\sin\theta$$ Note that because $\arctan$ only takes values in $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$, 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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