How do you write the polar equation $r = 2 csc θ$ $r=2csctheta$ in rectangular form?

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Answer 1 · 2016-11-27T02:19:36

I found: $y = 2$ $y=2$

I first rearranged the given equation:
$r = 2 csc (θ)$ $r=2csc(theta)$
$r = \frac{2}{sin (θ)}$ $r=2/sin(theta)$
$r sin (θ) = 2$ $rsin(theta)=2$

I then used the conversion formulae to change from polar to rectangular as follows:
$x = r cos (θ)$ $x=rcos(theta)$
$y = r sin (θ)$ $y=rsin(theta)$

Using the second of the above into our expression $r sin (θ) = 2$ $rsin(theta)=2$ we se that:
$y = 2$ $y=2$

How do you write the polar equation r=2cscthetar=2cscθr=2csctheta in rectangular form?