How do you convert #r csc theta = 8# to rectangular form?

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Answer 1 · 2016-05-13T03:55:52

#x^2+y^2-8y=0#

Relation between polar form #(r,theta)# and rectangular form #(x,y)# is given by

#rcostheta=x#, #rsintheta=y#, #r^2=a^2+b^2# and #tantheta=b/a#

Hence #rcsctheta=8# can be written as

#r/sintheta=8# or

#r^2/(rsintheta)=8# or

#(x^2+y^2)/y=8# or #x^2+y^2=8y# or

#x^2+y^2-8y=0#

This is the equation of a circle.

graph{x^2+y^2-8y=0 [-20, 20, -10, 10]}