How do you convert #r = -sin3θ# into rectangular form?

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Answer 1 · 2016-09-25T07:25:49

We know the relations

#x=rcostheta and y =rsintheta#

where r and #theta# are the polar coordinate of a point having rectangular coordinate #(x,y)#
So #r^2=x^2+y^2#

Now the given relation is

#r=-sin3theta=4sin^3theta-3sintheta#

#=>r^4=4r^3sintheta-3r^3sintheta#

#=>r^4=4(rsintheta)^3-3r^2*rsintheta#

#=>(x^2+y^2)^2=4y^3-3(x^2+y^2)y#

This is the rectangular form of the given polar equation.