How do you convert $r = 2 csc θ$ $r=2csctheta$ to rectangular form?

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Answer 1 · 2016-05-24T06:25:49

$y = 2$ $y=2$

To convert polar coordinates $(r, θ)$ $(r,theta)$ to rectangular coordinates $(x, y)$ $(x,y)$ the relation is

$x = r cos θ$ $x=rcostheta$ , $y = r sin θ$ $y=rsintheta$ , $r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$

Hence $r = 2 csc θ$ $r=2csctheta$ is equivalent to

$r = \frac{2}{sin θ} = \frac{2}{\frac{y}{r}}$ $r=2/sintheta=2/(y/r)$ or

$r = 2 \frac{r}{y}$ $r=2r/y$ or $y = 2$ $y=2$

How do you convert r=2cscthetar=2cscθ r=2csctheta to rectangular form?