How do you convert $r = cot θ csc θ$ $r=cotthetacsctheta$ into cartesian form?

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Answer 1 · 2016-06-29T17:46:11

$y^{2} = x$ $y^2 = x$

you know that

$x = r cos θ$ $x = r cos theta$
$y = r sin θ$ $y =r sin theta$

and

$cot θ csc θ = \frac{cos θ}{sin θ} \cdot \frac{1}{sin θ}$ $cot theta csc theta = cos theta / sin theta * 1 / sin theta$

so

$r = \frac{\frac{x}{r}}{\frac{y}{r}} \cdot \frac{1}{\frac{y}{r}} = \frac{x r}{y^{2}}$ $r = (x/r)/(y/r)*1/(y/r) = (xr)/y^2$

or $y^{2} = x$ $y^2 = x$

How do you convert r=cotthetacscthetar=cotθcscθr=cotthetacsctheta into cartesian form?