How do I convert this to rectangular form? r=5cot θ csc θ

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Answer 1 · 2018-07-13T15:04:54

The rectangular form is $y^2=x$

The polar form is

$r=cotthetacsctheta$

To convert to rectangular coordinates, apply the following

${(costheta=x/r),(sintheta=y/r), (r^2=x^2+y^2):}$

Rewrite the polar form as :

$r=cottheta*csctheta=costheta/sintheta*1/sintheta$

$=costheta/sin^2theta$

Therefore,

$rsin^2theta=costheta$

$r*y^2/r^2=x/r$

$y^2/r=x/r$

$y^2=x$

This is a parabola

graph{y^2-x=0 [-10, 10, -5, 5]}