Polar / Rectangular Coordinates

[Sparky_]

Homework Statement

Convert into rectangular coordinates:

<br /> r = tan(theta)<br />

Homework Equations

The Attempt at a Solution

<br /> r = \frac {sin}{cos}<br />


I used
<br /> r = \sqrt{x^2+y^2}<br />
and

<br /> cos = \frac {x}{r}<br /> <br /> x = (r)(cos)<br /> sin = \frac {y}{r}<br /> <br /> y = (r)(sin)<br />

<br /> \sqrt {x^2+y^2} = \frac{\frac{y}{\sqrt {x^2+y^2}}}{\frac{x}{\sqrt {x^2+y^2}}}<br />

Then -

<br /> x\sqrt {x^2+y^2} -y =0<br />

The book gets
<br /> x^4 + (x^2)(y^2) - y^2 <br /> <br />


Can you help with the simplification to get to the book’s answer?

Thanks
-Sparky

 

[chaoseverlasting]

Take y to the other side, square and open brackets.

 

[Sparky_]

Thanks so much!