Proper description of a polar region in xy plane

Question

If $$0\leq\theta\leq \pi/2, ~~1\leq r\leq 2$$ so which picture is right? I myself selected the one on the right. However, someone preferred to take the other picture because those two line belongs to the mentioned angels.

Thanks

Answer 1

When dealing with polar functions $r=f(\theta)$, $r$ may be (and usually is) allowed to go negative. However, when describing regions of the plane, conventionally $r$ is always non-negative to avoid a double cover of the $\theta$ parameter space, so the right picture is right.