# Thread: Convert polar to rectangular

1. ## Convert polar to rectangular

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

$r= csc (\theta )$

I do not know how to do this.

I have
$y= r*sin (\theta )$ and
$x= r*cos (\theta )$

$y= csc(\theta )*sin (\theta )$
$y=1$

and

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

But how do I find the asymptotes and how does the curve looks like?
Thanks for any help

2. It's not clear to me what you are doing here. You have NOT written the equation in rectangular coordinates.

The equation, in polar coordinates is $r= csc(\theta)= \frac{1}{sin(\theta)}$. To get " $r sin(\theta)$", which we could immediately write as "y", divide both sides of the equation by r: $1= \frac{1}{r sin(\theta)}= \frac{1}{y}$ so the equation becomes $\frac{1}{y}= 1$ which is the same as $y= 1$, a horizontal straight line.