Answer
Symmetrical about the polar axis
Work Step by Step
The rules for symmetry:
1. About the Polar Axis if the graph is the same when replacing θ with -θ
2. About the pole if the graph is the same when replacing r with -r or θ by $θ + \pi$
3. About the vertical line $θ = \frac{\pi}{2}$ if the graph is the same when replacing θ by $\pi - θ$
Given $r = 3 \sec θ$
$r = \frac {3}{\cos θ}$
1. $r = \frac {3}{\cos (-θ)}= \frac {3}{\cos θ}$
Yes, the same!
2. $-r = \frac {3}{\cos θ} = -\frac {3}{\cos θ}$
Not the same, so not about the pole
3. $r = \frac {3}{\cos (\pi - θ)} = \frac {3}{-\cos θ}$
Not the same, so not about the vertical line $θ = \frac{\pi}{2}$
Symmetrical about the polar axis