I am trying to convert the equation $y=4/x$ into a polar equation.
I have done this work but I am not sure if it is right. I just subsituted $r\sin(\theta)$ for $y$ and $r\cos(\theta)$ for $x$ and solved for $r$ , which gave me $r = \sqrt{4\over (\sin(\theta)\cdot\cos(\theta))}$.
Is this correct? Or am I going about this all wrong? Thanks in advance.
Best Answer
Yes. You have $xy = 4$ in cartesian coordinates, so in polar coordinates that is indeed: $$r^2\sin(\theta)\cos(\theta) =4$$
You can leave it at that, or rearrange to suit. I recommend using $ 2\sin(\theta)\cos(\theta)=\sin(2\theta)$ .
$$r^2\,\sin(2\theta) = 8$$
$$r = +2\sqrt{2\csc(2\theta)}$$