r = 2 + sin2θ convert to polar? (i know the conversion stuff i just cant get it right)?

anonymousanonymous
in Science & Mathematics

I seriously am stressing over this problem, ive looked up all kinds of tutorials and every time i try this problem i get x^2 + y^2 = 2r + 2y but i cant get any further.

Comments

  • northstarnorthstar

    It already is polar. I assume you mean, "Convert to Cartesian".

    r = 2 + sin(2θ)

    __________

    Remember the identities.

    x = rcosθ

    y = rsinθ

    x² + y² = r²

    ___________

    r = 2 + sin(2θ)

    r = 2 + 2(sinθ)(cosθ)

    r = 2 + 2(y/r)(x/r)

    r = 2 + 2xy/r²

    Multiply thru by r².

    r³ = r² + 2xy

    (x² + y²)^(3/2) = (x² + y²) + 2xy

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