Polar / Rectangular Coordinates

[Sparky_]

Homework Statement

Convert into rectangular coordinates:

[tex]
r = tan(theta)
[/tex]

Homework Equations

The Attempt at a Solution

[tex]
r = \frac {sin}{cos}
[/tex]


I used
[tex]
r = \sqrt{x^2+y^2}
[/tex]
and

[tex]
cos = \frac {x}{r}

x = (r)(cos)
sin = \frac {y}{r}

y = (r)(sin)
[/tex]

[tex]
\sqrt {x^2+y^2} = \frac{\frac{y}{\sqrt {x^2+y^2}}}{\frac{x}{\sqrt {x^2+y^2}}}
[/tex]

Then -

[tex]
x\sqrt {x^2+y^2} -y =0
[/tex]

The book gets
[tex]
x^4 + (x^2)(y^2) - y^2

[/tex]


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!