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]}