Answer
$r_y$ is greatest in magnitude at $\theta = 90^{\circ}$ and $\theta = 270^{\circ}$
Work Step by Step
At $\theta = 90^{\circ}$, the magnitude of $r_y$ is $r$ which is the maximum possible for the the vertical component $r_y$ of the position vector
At $\theta = 270^{\circ}$, the magnitude of $r_y$ is $r$ which is the maximum possible for the the vertical component $r_y$ of the position vector
$r_y$ is greatest in magnitude at $\theta = 90^{\circ}$ and $\theta = 270^{\circ}$
