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how do you convert r=1+3sin2x from a polar equation to a rectangular equation

Your eqn is a little confusing. Normally, the variable r in polar coordinates is the distance of a point f(r,theta) from the origin (theta is the angle relative to the x axis, measured positive counter-clockwise). The variable r is thus a positive quantity, ususally

r = sqrt(x^2 + y^2), x & y real.

As you can see, in your formula, there are values of x for which r < 0. Even if x is supposed to be the angle theta, we run into the same problem unless the domain of theta (allowable values) is restricted. Did you copy the problem correctly? Let me know in a follow-up.

Randy

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