# Convert polar to rectangular

• Mar 31st 2010, 10:25 AM
DBA
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.

$\displaystyle r= csc (\theta )$

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
• Mar 31st 2010, 12:39 PM
HallsofIvy
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 $\displaystyle r= csc(\theta)= \frac{1}{sin(\theta)}$. To get "$\displaystyle r sin(\theta)$", which we could immediately write as "y", divide both sides of the equation by r: $\displaystyle 1= \frac{1}{r sin(\theta)}= \frac{1}{y}$ so the equation becomes $\displaystyle \frac{1}{y}= 1$ which is the same as $\displaystyle y= 1$, a horizontal straight line.