Convert polar to rectangular

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March 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.

$r= csc (\theta )$

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
March 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 $r= csc(\theta)= \frac{1}{sin(\theta)}$ . 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.

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