Question

How do I convert this polar equation to a rectangular equation? r=-4sintheta

Answer 1

Okay, here we have this:

Considering the provided polar equation, we are going to convert it to a rectangular equation, so we obtain the following:

Start by multiplying both sides by r.

$\begin{gathered} r=-4sin(\theta) \\ r^2=-4rsin(\theta) \end{gathered}$

Remember that r²=x²+y²:

$x^2+y^2=-4r\sin (\theta)$

Keep in mind that y=rsinθ:

$\begin{gathered} x^2+y^2=-4y \\ x^2+y^2+4y=0 \end{gathered}$

And finally we complete the square:

$\begin{gathered} x^2+(y^2+4y+4)=4 \\ x^2+(y+2)^2=4 \end{gathered}$

The last equation is the rectangular equation we were looking for.