How do you convert $r = 2 sin t$ $r = 2sint$ into a rectangular equation?

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Answer 1 · 2015-11-27T19:18:34

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

Multiply both sides by $r$ $r$ :

$r^{2} = 2 r sin (t)$ $r^2 = 2rsin(t)$ .

Since $r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$ and $y = r sin (t)$ $y=rsin(t)$ , the equation becomes

$x^{2} + y^{2} = 2 y$ $x^2+y^2 = 2y$ , which you can rewrite as $x^{2} + y^{2} - 2 y = 0$ $x^2+y^2-2y=0$

How do you convert r = 2sintr=2sint r = 2sint into a rectangular equation?