# How do you convert the polar equation 10 sin(θ) to the rectangular form?

Feb 2, 2015

I suppose that your complete equation might be:
$r = 10 \sin \left(\theta\right)$
To change it in rectangular form you must remember that a point $P$ can be represented by:
1) rectangular coordinates $x \mathmr{and} y$ (on your axes);
2) polar coordinates: a length $r$ and an angle $\theta$;

In your case we can multiply both sides by $r$:
${r}^{2} = 10 r \sin \left(\theta\right)$
Substituting for ${r}^{2}$ and $r \sin \left(\theta\right)$ from the above expressions we get:
${x}^{2} + {y}^{2} = 10 y$
in rectangular form.

The graph of your equation is: