How do you convert $r = 3 sin (θ)$ $r = 3sin(theta)$ into a cartesian equation?

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Answer 1 · 2015-09-22T20:21:36

Use $r = \sqrt{x^{2} + y^{2}}$ $r = sqrt(x^2+y^2)$ and $sin (θ) = \frac{y}{r}$ $sin(theta) = y / r$ to get:

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

$r = \sqrt{x^{2} + y^{2}}$ $r = sqrt(x^2+y^2)$ and $sin (θ) = \frac{y}{r}$ $sin(theta) = y / r$

So $r = 3 sin (θ)$ $r = 3sin(theta)$ becomes:

$\sqrt{x^{2} + y^{2}} = \frac{3 y}{\sqrt{x^{2} + y^{2}}}$ $sqrt(x^2+y^2) = (3y)/sqrt(x^2+y^2)$

Multiply both sides by $\sqrt{x^{2} + y^{2}}$ $sqrt(x^2+y^2)$ to get:

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

graph{x^2+y^2-3y=0 [-4.913, 5.087, -0.98, 4.02]}

How do you convert r = 3sin(theta)r=3sin(θ)r = 3sin(theta) into a cartesian equation?