How do you convert $r^2 = cost$ to rectangular form?

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Answer 1 · 2016-12-04T17:43:59

$(x^2+y^2)^(3/2)-x =0$

We have:

$x=rcost$
$y=rsint$

and from this we can derive:

$x^2+y^2 = r^2$

$cost = x/r =+- x/sqrt(x^2+y^2)$

We can se from the equation that $cost$ must always be positive (as it equals $r^2$ ), so we take the positive sign of the square root, and have:

$(x^2+y^2) = x/sqrt(x^2+y^2)$

or:

$(x^2+y^2)^(3/2)-x =0$

How do you convert r^2 = costr^2 = cost to rectangular form?