Convert the polar equation to rectangular coordinates. (use variables x and y as needed.)

r = 7 csc θ

I will list first the important conversions and identities that are essential for the solution:

r^2 = x^2 + y^2
x = rcostheta
y = rsintheta

These are the equations when you convert between rectangular and polar coordinates. Also csc theta = 1/sin theta fromtrigo identities. Thus, substituting these equations would yield:

r = 7 csctheta
r = 7/sin theta
√(x^2 + y^2) = 7/(y/r)
√(x^2 + y^2) = 7r/y
y√(x^2 + y^2) = 7r

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