Polar / Rectangular Coordinates

[Sparky_]

Homework Statement

Convert into rectangular coordinates:

$$r = tan(theta)$$

Homework Equations

The Attempt at a Solution

$$r = \frac {sin}{cos}$$


I used
$$r = \sqrt{x^2+y^2}$$
and

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

$$\sqrt {x^2+y^2} = \frac{\frac{y}{\sqrt {x^2+y^2}}}{\frac{x}{\sqrt {x^2+y^2}}}$$

Then -

$$x\sqrt {x^2+y^2} -y =0$$

The book gets
$$x^4 + (x^2)(y^2) - y^2$$


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!