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

$\displaystyle r= csc (\theta ) $

I do not know how to do this.

I have

$\displaystyle y= r*sin (\theta ) $ and

$\displaystyle x= r*cos (\theta ) $

$\displaystyle y= csc(\theta )*sin (\theta ) $

$\displaystyle y=1$

and

$\displaystyle x= csc(\theta )*cos (\theta ) $

$\displaystyle x= \frac{cos (\theta ) }{sin (\theta )} = tan (\theta )$

But how do I find the asymptotes and how does the curve looks like?

Thanks for any help