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Homework Help: Convert the polar equation to rectangular form.

  1. Jan 5, 2014 #1
    1. The problem statement, all variables and given/known data

    r = 3sin[itex]\theta[/itex]


    x= rcos[itex]\theta[/itex]

    x = 3sin[itex]\theta[/itex]cos[itex]\theta[/itex]

    and since:

    y = rsin[itex]\theta[/itex]

    y = 3[itex]sin^2\theta[/itex]

    Then I'm sort of stuck..
  2. jcsd
  3. Jan 5, 2014 #2


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    You are making it way too difficult. Put ##\sin\theta =\frac y r## in your first equation then see if you can get an xy equation from that.
  4. Jan 5, 2014 #3


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    Try putting sinθ=y/r.
  5. Jan 6, 2014 #4

    Like so:

    r = 3sinθ becomes (r=3[itex]\frac{y}{r}[/itex])

    = (r =[itex]\sqrt{3y}[/itex]) ?

    or solving for y, (y = [itex]\frac{r^2}{3}[/itex])

    or do you mean something like this:

    ([itex]\frac{y}{r} = sinθ [/itex]) becomes ([itex]\frac{y}{3sinθ} = sinθ[/itex])

    = (y = 3sin[itex]^{2}θ[/itex])
  6. Jan 6, 2014 #5


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    You also want to use ##r^2=x^2+y^2##. You need to express both ##sin(\theta)## and r in terms of x and y. Try once more.
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