MHB 639.7.6.97 write an equivalent polar equation

[karush]

$\textrm{write an equivalent polar equation}$
\begin{align*}\displaystyle
x^2+(y-1)^2&=1
\end{align*}
$\textrm{expand and rearrange}$
$$x^2+y^2=2y$$
$\textrm{substitute $r^2$ for $x^2+y^2$
and $r \cos(\theta)$ for $y$}$
$\textrm{then}$
$$r^2=2r\cos(\theta)$$
$\textrm{or}$
$$r=2 \cos(\theta)$$

kinda maybe

 

[MarkFL]

Looks good to me. (Yes)

edit: On second thought...there is an issue...$2y=2r\sin(\theta)$...:D

 

[karush]

got it.

should of seen that

- - - Updated - - -

$\textrm{write an equivalent polar equation}$
\begin{align*}\displaystyle
x^2+(y-1)^2&=1
\end{align*}
$\textrm{expand and rearrange}$
$$x^2+y^2=2y$$
$\textrm{substitute $r^2$ for $x^2+y^2$
and $r \cos(\theta)$ for $y$}$
$\textrm{then}$
$$r^2=2r\sin(\theta)$$
$\textrm{or}$
$$r=2 \sin(\theta)$$