Pre-Calc

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Can you show me how to find the rectangular equation of r=2costheta + 3 sin theta
All I need is an example to work off I was absent today from Pre-Calc and I have homework to do and no explanation with them-Please help with this one Thank you

  • Pre-Calc -

    what the heck is a rectangular equation?

  • Pre-Calc -

    hmm. you have given a polar coordinates equation, and want it y = f(x)?

    cos theta = x/r
    sin theta = y/r

    r^2 = x^2 + y^2

    r^2 = (2 cos t + 3 sin t)^2
    = 4 cos^2 t + 12 sin t cos t + 9 sin^2 t
    = 4 x^2/r^2 + 12xy/r^2 + 9y^2/r^2
    r^4 = 4x^2 + 12xy + 9y^2

    so, *x^2 + y^2)^2 = 4x^2 + 12xy + 9y^2

    Not a pretty sight. The curve is cool, though

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