How do you convert the polar equation $r=3sintheta$ into rectangular form?

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Answer 1 · 2016-10-05T15:27:20

$x^2+(y-3/2)^2=9/4$

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

Multiply the equation by $r$

$r*r=3rsin(theta)$

Simplify

$r^2=3rsin(theta)$

Make appropriate substitutions

$x^2+y^2=3y$

Gather all of the terms to the same side

$x^2+y^2-3y=0$

Complete square using the coefficient of $y$ variable

$(-3/2)^2=9/4$

Add $9/4$ to both sides the equation to keep it balanced. The constant $9/4$ allows you make a perfect square trinomial.

$x^2+y^2-3y+9/4=9/4$

Rewrite

$x^2+(y-3/2)^2=9/4$

Check out a tutorial on converting an equation from polar to rectangular

Check out a tutorial on completing the square graphically

Check out a tutorial on completing the square analytically

How do you convert the polar equation r=3sinthetar=3sintheta into rectangular form?