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    The intrinsic equation of a curve is s=12sin²(phi) where s is measured from the point (-8,0).
    Show that x^2/3 + y^2/3 = 4 is the cartesian equation of the curve.

    I don't even know where to start and have resorted to praying that nothing even remotely like this comes up on the exam tomorrow. I don't know how to convert from intrinsic to cartesian in general and there aren't any examples of it in the book. Can somebody please tell me where to start and what to do cos i really don't understand it.
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    You need to derive some some parametric equations to find both x and y in terms of psi. In general if I have an intrinsic equation, s = g(p) where p = psi, and I want to find an equation for y in terms of p I would note first that

    dy/ds = sin(p)
    y = INT sin(p) ds

    Now, ds/dp = g'(p), therefore

    y = INT sin(p) ds = INT sin(p) (ds/dp) dp
    y = INT g'(p) sin(p) dp

    You can use the fact that dx/ds = cos(p) to find an equation for x in terms of p. Evaluating the integrals will give you parametric equations. You should be able to apply the above ideas to your example. I hope this helps.
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    Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thank you. Thanks
 
 
 
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Updated: June 20, 2004

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