Answer
In general, the completed statements in parts (a)-(e) mean that the graphs of polar equations of the form $r = a \pm b~sin~\theta$ (where $a$ may be 0) are symmetric with respect to the vertical line $\theta = \frac{\pi}{2}$
Work Step by Step
Note that $~~sin~(\pi-\theta) = sin~\theta$
According to part (b), the graph of $r = f(\theta)$ is symmetric with respect to the vertical line $\theta = \frac{\pi}{2}$ if substitution of $\pi-\theta$ for $\theta$ leads to an equivalent equation.
In general, the completed statements in parts (a)-(e) mean that the graphs of polar equations of the form $r = a \pm b~sin~\theta$ (where $a$ may be 0) are symmetric with respect to the vertical line $\theta = \frac{\pi}{2}$
