How do you convert $r = 4 sin θ$ $r=4sin theta$ into cartesian form?

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Answer 1 · 2017-02-04T14:24:03

$x^{2} + y^{2} - y = 0$ $x^2+y^2-y=0$

for polar to and from Cartesian the equations are

$r^{2} = x^{2} + y^{2}$ $r^2=x^2+y^2$

$x = r cos θ$ $x=rcostheta$

$y = r sin θ$ $y=rsintheta$
$:.r=4sintheta " multiply through by "r$

$r^2=rsintheta$

substituting back using the above conversions

$x^2+y^2=4y$

$x^2+y^2-4y=0$

graph{x^2+y^2=4y [-10, 10, -5, 5]} this is a circle centre $(0,2)$ radius $=2$

How do you convert r=4sin thetar=4sinθr=4sin theta into cartesian form?