Change from polar to rectangular coordinates

[duki]

Homework Statement

change from polar to rectangular coordinates

Homework Equations

$$\cos{theta}+r^2\sin{theta}=\tan{theta}$$

The Attempt at a Solution

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

does that look right?

 

[mutton]

Since $$r^2$$ is multiplied by $$\sin \theta$$ rather than added to it, shouldn't it be

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

 

[duki]

ooohh thanks

 

[HallsofIvy]

The simplest way to do this is to multiply the entire equation by r:
$$r cos(\theta)+ r^2(r sin(\theta))= r tan(\theta)= r \frac{r sin(\theta)}{r cos(\theta)}$$
so
$$x+ (x^2+ y^2)y= \sqrt{x^2+ y^2}\frac{y}{x}$$