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

Feb 4, 2017

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

Explanation:

for polar to and from Cartesian the equations are

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

$x = r \cos \theta$

$y = r \sin \theta$
$\therefore r = 4 \sin \theta \text{ multiply through by } r$

${r}^{2} = r \sin \theta$

substituting back using the above conversions

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

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

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