Sorry for this question but I want to be get clarified. Lets look at the image below.
My question is this. Why not include the point of origin when in fact the polar coordinates $(0,1\ \text{rad})$ refers to $(x,y)=(0,0)$? I might be receiving downvotes for this but its then okay. What I understand is that in the Polar Coordinate System, $-\infty < r < \infty$ so that the graph that represent to $\theta =1$ is a line that passes through the point of origin with an angle of inclination equal to 1 radian.