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.

How do you convert r = -sin3θr = -sin3θ into rectangular form?