Advanced Math/Pre-Calc

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

Answer
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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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

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