How to convert from cartesian to polar equation with no intercept

Question

I want to convert the equation $y=2x$ from cartesian form to polar form. I found already a couple of other topics regarding this f.e.Polar Coordinate function of a Straight Line

but they all have a the function in the form of $y = mx+c$ Since I have no $c$ and i use the convertion formulas $y = r \sin(t)$ and $x = r \cos(t)$ when substituting

I get

$r \sin(t) = 2 r \cos(t)$

and then the $ r$ can be scrapped leading to

$\sin(t) = 2 \cos(t)$

or $0 = 2\cos(t)/\sin(t)$

What am I doing wrong?

Answer 1

Your algebra is incorrect. The proper rearrangement of the equation $$\sin \theta = 2 \cos \theta$$ is$$ \tan \theta = 2.$$