Test the graph of the following equation for symmetry with respect to $\theta = \frac { \pi } { 2 }$, the polar axis, and the pole.
$$r = - 2 + \sin ( 2 \theta )$$
A) The graph is symmetric with respect to $\theta = \frac { \pi } { 2 }$ only.
B) The graph is symmetric with respect to the pole only.
C) The graph is symmetric with respect to all three.
D) The graph has no symmetries.
E) The graph is symmetric with respect to the polar axis only.

Question

Quizplus · Accepted Answer

The graph is symmetric with respect to the pole because replacing $\theta$ with $-\theta$ or $\pi + \theta$ in the equation $r = -2 + \sin(2\theta)$ results in the original equation, indicating pole symmetry. It does not exhibit symmetry with respect to $\theta = \frac{\pi}{2}$ or the polar axis, as these transformations do not preserve the equation in a way that indicates such symmetries.

Test the Graph of the Following Equation for Symmetry with Respect