Find the asymptotes by expressing the rectangular coordinates x and y as function of theta, then sketch the curve in polar.

$\displaystyle

r= cot (\theta )

$

$\displaystyle

y= r*sin (\theta )

$

$\displaystyle

x= r*cos (\theta )

$

$\displaystyle

r= cot(\theta)

$

$\displaystyle

r= \frac{cos(\theta)}{sin(\theta)} $ |multipy both sides by $\displaystyle sin(\theta)$

$\displaystyle

r sin(\theta) = \frac{cos(\theta)}{sin(\theta)} sin(\theta)

$

$\displaystyle

y = cos(\theta)

$

How do I get the horizontal asymptote from here?

Then

$\displaystyle

r= cot(\theta)

$

$\displaystyle

r= \frac{cos(\theta)}{sin(\theta)} $ |multipy both sides by $\displaystyle cos(\theta)$

$\displaystyle

r cos(\theta) = \frac{cos(\theta)}{sin(\theta)} cos(\theta)

$

$\displaystyle

x= \frac{cos^{2}(\theta)}{sin(\theta)}

$

How do I get the vertical asymptote from here?

Thanks!