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Math Help - Convert polar to rectangular

  1. #1
    DBA
    DBA is offline
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    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
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  2. #2
    MHF Contributor

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    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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