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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
Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 9 Politeness = 10 Comment Thanks Randy, your responce helped me to come up with the correct answer.

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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography