How do you convert the polar equation $r=2sintheta$ into rectangular form?

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Answer 1 · 2016-11-19T02:50:30

Please see the explanation.

Multiply both sides by r:

$r^2 = 2rsin(theta)$

Substitute $x^2 + y^2$ for $r^2$

$x^2 + y^2 = 2rsin(theta)$

Substitute y for $rsin(theta)$

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

Add $k^2 - 2y$ to both sides:

$x^2 + y^2 - 2y + k^2 = k^2$

$k = 1$ completes the square:

$x^2 + (y - 1)^2 = 1^2$

Insert a zero in the x term:

$(x - 0)^2 + (y - 1)^2 = 1^2$

Standard form for the equation of a circle with a center of $(0,1)$ and a radius of 1.

How do you convert the polar equation r=2sinthetar=2sintheta into rectangular form?